An integral lift of the Gammagenus
An integral lift of the Gammagenus

Jack Morava, Johns Hopkins University
Fine Hall 314
The Hirzebruch genus of a complexoriented manifold $M$ associated (by Kontsevich) to Euler's Gammafunction 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 homotopytheoretic terms, it is the homomorphism $\mu \rightarrow \mu_{MSp} KO$ 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.