Elliptic Cohomology

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.

List of contents

Elliptic Genera.- Cohomology Theory Ell*(X).- Work of M. Hopkins, N. Kuhn, and D. Ravenel.- Mathieu Groups.- Cohomology of Certain Simple Groups.- Ell*(BG) - Algebraic Approach.- Completion Theorems.- Elliptic Objects.- Variants of Elliptic Cohomology.- K3-Cohomology.

Product details

• Authors: Charles B Thomas, Charles B. Thomas
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.07.2009
• EAN: 9780306460975
• ISBN: 978-0-306-46097-5
• No. of pages: 200
• Dimensions: 171 mm x 236 mm x 20 mm
• Weight: 481 g
• Illustrations: XII, 200 p.
• Series: University Series in Mathematics; University Series in Mathematics
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Geometry