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Manifolds and Modular Forms, Vol. E20

Manifolds and Modular Forms (Aspects of Mathematics)

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Manifolds and Modular Forms, Vol. E20

Manifolds and Modular Forms (Aspects of Mathematics)

4.85 33,274 ratings · 5,269 reviews
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Overview: During the winter term 1987/88 I gave a course at the University of Bonn under the title "Manifolds and Modular Forms." Iwanted to develop the theory of "Elliptic Genera" and to leam it myself on this occasion. This theory due to Ochanine, Landweber, Stong and others was relatively new at the time. The word "genus" is meant in the sense of my book "Neue Topologische Methoden in der Algebraischen Geometrie" published in 1956: A genus is a homomorphism of the Thom cobordism ring of oriented compact manifolds into the complex numbers. Fundamental examples are the signature and the A-genus. The A-genus equals the arithmetic genus of an algebraic manifold, provided the first Chem class of the manifold vanishes. According to Atiyah and Singer it is the index of the Dirac operator on a compact Riemannian manifold with spin structure. The elliptic genera depend on a parameter. For special values of the parameter one obtains the signature and the A-genus. Indeed, the universal elliptic genus can be regarded as a modular form with respect to the subgroup r (2) of the modular group; the two cusps o giving the signature and the A-genus. Witten and other physicists have given motivations for the elliptic genus by theoretical physics using the free loop space of a manifold.

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ISBN
3450448
Publication date
January 1, 1992
Pages
N/A pages
Reading Options
PDF · EPUB · Mobi
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Friedrich Hirzebruch
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Friedrich Hirzebruch is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Friedrich Hirzebruch enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Nancy Jones
Nancy Jones December 30, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Laura Clark
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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I was completely blown away. 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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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Laura Lopez
Laura Lopez June 17, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Melissa Baker
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Ashley Edwards
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A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Brian Wright
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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.
Donna Jackson
Donna Jackson November 13, 2025
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Laura Reyes
Laura Reyes May 11, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Kimberly Clark
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Cynthia Phillips
Cynthia Phillips July 06, 2024
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 very distinguished novel.
Michael Roberts
Michael Roberts September 13, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Kevin Carter
Kevin Carter July 24, 2024
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.
Betty Clark
Betty Clark March 04, 2025
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 solid 4 stars from me.
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I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
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I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Such a rich narrative. 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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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Donald King
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Joshua Thomas
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Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
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Mary Jones November 08, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Rebecca Carter
Rebecca Carter November 11, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Susan Lee
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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.
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Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Nancy Turner
Nancy Turner March 30, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Mary Thomas
Mary Thomas March 07, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Melissa Edwards
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Emily Clark
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Linda Hill
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Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Carol Hernandez
Carol Hernandez March 27, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Kimberly Mitchell
Kimberly Mitchell February 24, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Lisa Johnson
Lisa Johnson December 29, 2025
Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Barbara Perez
Barbara Perez October 04, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Jennifer Allen
Jennifer Allen April 28, 2025
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perhaps more aligned with a different audience's tastes.
Karen King
Karen King November 17, 2025
A decent, if standard, experience. It verged on repetitive in the second act. A more concise edit would have served it well. Perhaps more aligned with a different audience's tastes.
Mark Martin
Mark Martin September 30, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Mark Martin
Mark Martin April 22, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Anthony Turner
Anthony Turner October 23, 2025
An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Suitable if your reading queue is empty.
Linda  Davis
Linda Davis June 22, 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.
Edward King
Edward King April 02, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Betty Adams
Betty Adams October 17, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
Cynthia Phillips
Cynthia Phillips May 29, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Emily Hernandez
Emily Hernandez May 17, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Karen Thomas
Karen Thomas September 13, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Amanda Mitchell
Amanda Mitchell February 03, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Charles Thompson
Charles Thompson May 14, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Laura Clark
Laura Clark May 23, 2025
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Amanda Gomez
Amanda Gomez July 13, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Thomas Roberts
Thomas Roberts August 15, 2025
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.
Joseph Edwards
Joseph Edwards April 29, 2025
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Christopher Green
Christopher Green March 29, 2025
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Anthony Taylor
Anthony Taylor September 12, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Sarah Wright
Sarah Wright March 17, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Donna Jackson
Donna Jackson April 14, 2025
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.
Patricia Taylor
Patricia Taylor September 05, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Karen  Parker
Karen Parker January 10, 2025
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty.
Nicholas Cruz
Nicholas Cruz June 21, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Gary Flores
Gary Flores April 07, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Laura Cruz
Laura Cruz May 05, 2024
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Gary King
Gary King September 11, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Jessica Campbell
Jessica Campbell June 08, 2025
Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Michael Allen
Michael Allen August 16, 2025
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
Sandra Perez
Sandra Perez August 02, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Suitable if your reading queue is empty.
Melissa Smith
Melissa Smith October 28, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
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