Elliptic Cohomology

By: Charles B. Thomas

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Hardcover | 31 May 1999

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220 Pages

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24.13 x 16.51 x 2.54

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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.

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Introduction	p. 1
Elliptic Genera	p. 7
Cohomology Theory Ell* (X)	p. 23
Work of M. Hopkins, N. Kuhn, and D. Ravenel	p. 35
Mathieu Groups	p. 49
Cohomology of Certain Simple Groups	p. 61
Ell[superscript *] (BG) - Algebraic Approach	p. 79
Completion Theorems	p. 103
Elliptic Objects	p. 119
Variants of Elliptic Cohomology	p. 143
K3-Cohomology	p. 159
Brown-Peterson Cohomology	p. 179
Cayley Projective Plane OP[superscript 2]	p. 183
Index of [Gamma][subscript 0](N) in SL[subscript 2](Z)	p. 187
References	p. 191
Index	p. 197
Table of Contents provided by Blackwell. All Rights Reserved.

Elliptic Cohomology

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Hardcover

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Defective items

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Other Editions and Formats

Paperback

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