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Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

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Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

Differential Geometry and Topology: Three-Manifold Invariants Using Symplectic Geometry of Representation Varieties

4.85 66,474 ratings · 8,471 reviews
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Overview: Many phenomena of three-manifolds are related to the representations of their fundamental groups. The authors of this book, using an investigation of the intersections of Lagrangian subvarieties in singular symplectic varieties, develop invariants associated with the more general Lie group, including SU(n). From a combinatorial approach related to Vassiliev's perspective on knot theory, a number of researchers have obtained a theory of "finite-type invariants" of three-manifolds. The authors show that their general representation-theoretic invariants are of the finite type. As a result, their invariants have surgery formulae and are intimately related to issues in mapping class groups, knot theory and quantum physics. On the other hand, some combinatorial invariants are given new geometrical meaning through these relations with the fundamental group.

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Book details & editions

ISBN
2498534
Publication date
October 1, 1999
Pages
200 pages
Reading Options
PDF · EPUB · Mobi
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S. Cappell
About the Author
S. Cappell
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S. Cappell writes contemporary fiction and has always been fascinated by character-driven stories. They hold a degree in English Literature and previously worked as an editor before transitioning to writing their own books. S. Cappell lives with their spouse and a very vocal rescue cat.

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Cynthia Moore
Cynthia Moore January 09, 2025
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
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David Rivera January 01, 2024
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A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Jennifer Adams
Jennifer Adams August 11, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A solid 4 stars from me.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Dorothy Rivera August 02, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
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Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
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Kenneth Wright January 21, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Nicholas Taylor
Nicholas Taylor March 12, 2024
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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Nicholas Edwards December 10, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Dorothy Adams
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Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Sarah Perez
Sarah Perez June 17, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
James Carter
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Michael Flores
Michael Flores October 21, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Sharon Mitchell
Sharon Mitchell April 29, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Richard Edwards
Richard Edwards September 02, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Dorothy Gonzalez
Dorothy Gonzalez August 29, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Karen Gomez
Karen Gomez July 15, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Rebecca Anderson
Rebecca Anderson March 28, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
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Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Deborah Green
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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Barbara Gonzalez
Barbara Gonzalez June 18, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Sarah Jackson
Sarah Jackson May 23, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Richard King
Richard King December 27, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Donna Ramirez
Donna Ramirez August 26, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
Sarah Adams
Sarah Adams November 24, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Sandra Carter
Sandra Carter April 13, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Anthony Adams
Anthony Adams January 14, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Charles Adams
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Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Laura King
Laura King April 12, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Gary Rodriguez
Gary Rodriguez September 03, 2025
Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Kenneth Hill
Kenneth Hill June 09, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Betty Moore
Betty Moore February 09, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Richard Brown
Richard Brown March 12, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Gary Hill
Gary Hill December 05, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Dorothy  Davis
Dorothy Davis October 29, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
James Lewis
James Lewis April 17, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A wonderful companion for a quiet weekend.
Christopher Jackson
Christopher Jackson September 16, 2025
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Karen Roberts
Karen Roberts April 01, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
William White
William White July 07, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Michelle Clark
Michelle Clark November 28, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Donna Evans
Donna Evans August 06, 2024
Not entirely to my refined tastes. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Amanda Diaz
Amanda Diaz April 03, 2024
I find myself somewhat conflicted. It verged on repetitive in the second act. A more concise edit would have served it well. Unlikely to reread, but a reasonable expenditure of time.
William Carter
William Carter October 03, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
James Lewis
James Lewis July 12, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Daniel Diaz
Daniel Diaz November 30, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Sharon Thomas
Sharon Thomas April 25, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Amanda Cruz
Amanda Cruz June 18, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Steven Hall
Steven Hall September 30, 2024
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Thomas Williams
Thomas Williams March 03, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Linda Wright
Linda Wright October 07, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Amanda Scott
Amanda Scott December 18, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Daniel Evans
Daniel Evans July 24, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Anthony Evans
Anthony Evans July 16, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Paul Ramirez
Paul Ramirez November 23, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
David Rivera
David Rivera March 30, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Edward Carter
Edward Carter December 10, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Gary Baker
Gary Baker April 18, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Sharon King
Sharon King May 30, 2025
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Elizabeth Robinson
Elizabeth Robinson November 01, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Amanda Nguyen
Amanda Nguyen June 12, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
George Harris
George Harris January 01, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Ashley Jones
Ashley Jones October 06, 2024
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Donna Ramirez
Donna Ramirez July 19, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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