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Elliptic Cohomology

  • Book
  • © 1999

Overview

Authors:
  1. Charles B. Thomas

    1. University of Cambridge, Cambridge, England

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Part of the book series: University Series in Mathematics (USMA)

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-ix
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  2. Introduction

    Pages 1-5

  3. Elliptic Genera

    Pages 7-21

  4. Cohomology Theory Ell*(X)

    Pages 23-33

  5. Work of M. Hopkins, N. Kuhn, and D. Ravenel

    Pages 35-47

  6. Mathieu Groups

    Pages 49-60

  7. Cohomology of Certain Simple Groups

    Pages 61-77

  8. Ell*(BG) — Algebraic Approach

    Pages 79-101

  9. Completion Theorems

    Pages 103-117

  10. Elliptic Objects

    Pages 119-142

  11. Variants of Elliptic Cohomology

    Pages 143-158

  12. K3-Cohomology

    Pages 159-178

  13. Back Matter

    Pages 179-199
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Keywords

About this book

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.

Authors and Affiliations

  • University of Cambridge, Cambridge, England

    Charles B. Thomas

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