3/31/2011

Jack Morava
Johns Hopkins University

An integral lift of the Gamma-genus

The Hirzebruch genus of a complex-oriented manifold M associated (by Kontsevich) to Euler's Gamma-function has an analytic interpretation as the index of a family of deformations of a Dirac operator, parametrized by the homogeneous space Sp/U; in more homotopy-theoretic terms, it is the homomorphism

MU --> MU \smash_{MSp} KO

of ring spectra. It also has an interpretation as a kind of equivariant Euler characteristic of the free loopspace of M, suitably polarized. There are further intriguing connections with the theory of asymptotic expansions, involving the values of the zeta function at odd positive integers.