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Elliptic Cohomology : University Series in Mathematics - Charles B. Thomas

Elliptic Cohomology

University Series in Mathematics

Hardcover Published: 31st May 1999
ISBN: 9780306460975
Number Of Pages: 200

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Elliptic cohomology is an extremely beautiful theory with both geometric and arithmetic aspects. The former is explained by the fact that the theory is a quotient of oriented cobordism localised away from 2, the latter by the fact that the coefficients coincide with a ring of modular forms. The aim of the book is to construct this cohomology theory, and evaluate it on classifying spaces BG of finite groups G. This class of spaces is important, since (using ideas borrowed from `Monstrous Moonshine') it is possible to give a bundle-theoretic definition of EU-(BG). Concluding chapters also discuss variants, generalisations and potential applications.

Introductionp. 1
Elliptic Generap. 7
Cohomology Theory Ell* (X)p. 23
Work of M. Hopkins, N. Kuhn, and D. Ravenelp. 35
Mathieu Groupsp. 49
Cohomology of Certain Simple Groupsp. 61
Ell[superscript *] (BG) - Algebraic Approachp. 79
Completion Theoremsp. 103
Elliptic Objectsp. 119
Variants of Elliptic Cohomologyp. 143
K3-Cohomologyp. 159
Brown-Peterson Cohomologyp. 179
Cayley Projective Plane OP[superscript 2]p. 183
Index of [Gamma][subscript 0](N) in SL[subscript 2](Z)p. 187
Referencesp. 191
Indexp. 197
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780306460975
ISBN-10: 0306460971
Series: University Series in Mathematics
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 200
Published: 31st May 1999
Publisher: Springer Science+Business Media
Country of Publication: US
Dimensions (cm): 24.13 x 16.51  x 2.54
Weight (kg): 0.48

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