Elliptic Cohomology

1999
ISBN: 978-0-306-46097-5
Verlag: Springer US

Buch, Englisch, 200 Seiten, HC runder Rücken kaschiert, Format (B × H): 157 mm x 235 mm, Gewicht: 1060 g

Reihe: University Series in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Thomas, Charles B.

Fachgebiete

• Mathematik | Informatik Mathematik Topologie Mengentheoretische Topologie
• Mathematik | Informatik Mathematik Geometrie Elementare Geometrie: Allgemeines
• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

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.