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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 69,878 ratings · 7,606 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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Published January 1, 1992
ISBN 3450448
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After spending years working in the corporate world, Friedrich Hirzebruch finally decided to pursue a lifelong passion for writing. They currently reside in a quiet suburb where they spend most of their time outlining new stories, reading extensively, and occasionally attempting to bake.

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Robert Smith
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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
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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.
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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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A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Absolutely brilliant. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
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Lisa Gomez October 07, 2025
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Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
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Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
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Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
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Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Thomas Campbell
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A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Amanda Perez
Amanda Perez September 11, 2025
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.
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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.
John Moore
John Moore March 09, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Kimberly Johnson
Kimberly Johnson May 15, 2024
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
Cynthia Ramirez
Cynthia Ramirez September 20, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Matthew Hernandez
Matthew Hernandez March 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.
Mark  Davis
Mark Davis November 03, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. A fair 3 stars.
Kimberly Johnson
Kimberly Johnson November 13, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Dorothy Robinson
Dorothy Robinson July 01, 2024
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.
Michelle Brown
Michelle Brown August 06, 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.
Susan Mitchell
Susan Mitchell December 05, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Richard Johnson
Richard Johnson February 02, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Emily Wilson
Emily Wilson November 01, 2024
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Christopher Evans
Christopher Evans April 09, 2024
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Jacob Rodriguez
Jacob Rodriguez May 05, 2024
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Joshua Evans
Joshua Evans May 14, 2024
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.
Joseph Phillips
Joseph Phillips May 21, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Edward Carter
Edward Carter March 09, 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.
Gary Moore
Gary Moore October 16, 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.
George Wright
George Wright November 28, 2024
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Steven Miller
Steven Miller August 04, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Elizabeth Clark
Elizabeth Clark December 24, 2025
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Gary Adams
Gary Adams August 14, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Anthony Campbell
Anthony Campbell January 07, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
William  Parker
William Parker January 10, 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. Quite impressive overall.
Gary Diaz
Gary Diaz June 21, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Joshua Taylor
Joshua Taylor February 26, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Michelle Ramirez
Michelle Ramirez January 06, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Emily Clark
Emily Clark January 09, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Karen Baker
Karen Baker January 05, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Emily Roberts
Emily Roberts September 27, 2025
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Eric Johnson
Eric Johnson November 01, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Carol Mitchell
Carol Mitchell January 11, 2024
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Jessica Adams
Jessica Adams December 08, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
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