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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 34,437 ratings · 8,574 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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Friedrich Hirzebruch
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Friedrich Hirzebruch is a writer and avid reader based in the Pacific Northwest. Before pursuing writing full-time, they spent over a decade working in education. When not working on their next book, Friedrich Hirzebruch can usually be found hiking with their dog or trying out new coffee shops in their neighborhood.

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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
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Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
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A profoundly satisfying read. 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. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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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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Such a rich narrative. 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. Worth every moment spent reading.
Donna Phillips
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A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Michelle Allen
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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 wonderful companion for a quiet weekend.
Barbara Lee
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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.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Joshua Rodriguez
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Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Linda Smith
Linda Smith March 02, 2025
It was adequate. Certain acts were fascinating, while others felt like a slight endeavor to complete. A fair 3 stars.
George Ramirez
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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.
Lisa Collins
Lisa Collins April 02, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Betty Lee
Betty Lee September 29, 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.
Susan Brown
Susan Brown December 27, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Jacob Young
Jacob Young November 02, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Gary Martin
Gary Martin November 24, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Andrew Campbell
Andrew Campbell November 08, 2025
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.
Mary  Davis
Mary Davis December 04, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Eric Flores
Eric Flores March 02, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Betty Martin
Betty Martin September 04, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Steven  Davis
Steven Davis March 22, 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.
Ryan Jones
Ryan Jones January 26, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Daniel Turner
Daniel Turner August 02, 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.
Kimberly Wright
Kimberly Wright May 28, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Laura Walker
Laura Walker July 18, 2024
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Melissa Nelson
Melissa Nelson May 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.
Nicholas Mitchell
Nicholas Mitchell May 23, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Mary Phillips
Mary Phillips October 27, 2024
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.
Nicholas Ramirez
Nicholas Ramirez August 29, 2025
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.
George Taylor
George Taylor June 27, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Rebecca Scott
Rebecca Scott May 17, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Donald Gomez
Donald Gomez October 10, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Mark Carter
Mark Carter July 28, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Joseph White
Joseph White February 26, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
George Miller
George Miller September 11, 2024
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.
Stephanie Miller
Stephanie Miller April 09, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Elizabeth Thompson
Elizabeth Thompson March 16, 2024
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.
Thomas Taylor
Thomas Taylor March 04, 2025
It was adequate. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
Michelle Walker
Michelle Walker December 01, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Richard White
Richard White August 10, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Barbara Campbell
Barbara Campbell April 03, 2025
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Eric Moore
Eric Moore June 15, 2024
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Anthony Wilson
Anthony Wilson January 24, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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