Elliptic Curves and Modular Forms in Algebraic Topology

Download or read book Elliptic Curves and Modular Forms in Algebraic Topology written by Peter S. Landweber and published by Springer. This book was released on 2006-11-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: A small conference was held in September 1986 to discuss new applications of elliptic functions and modular forms in algebraic topology, which had led to the introduction of elliptic genera and elliptic cohomology. The resulting papers range, fom these topics through to quantum field theory, with considerable attention to formal groups, homology and cohomology theories, and circle actions on spin manifolds. Ed. Witten's rich article on the index of the Dirac operator in loop space presents a mathematical treatment of his interpretation of elliptic genera in terms of quantum field theory. A short introductory article gives an account of the growth of this area prior to the conference.