Beyond the Elliptic Genus
Speaker: I. M. Singer, MIT
Location: Warren Weaver Hall 1302
Monday, April 19, 2010, 3:45 p.m. CANCELLED
A genus is a homomorphism Phi from a cobordism ring to a commutative ring R with unit. I'll begin with examples of F. Hirzebruch where R is the ring of integers. Then I'll describe some of the work of S. Ochanine and P.S. Landweber where R is the ring of modular forms for an elliptic curve, i.e., a Riemann surface with genus g=1; Phi is the elliptic genus.
I'll explain the physics derivation of the elliptic genus using the Dirac‐Ramond operator on loop space. That leads to a new cobordism ring, string cobordism, and a new genus with values in the ring of modular forms for surfaces with genus g>1.
I'll end with speculations on possible applications of this generalized string genus.
(Joint work with Orlando Alvarez.)