A Geometric Interpretation of the χ-{y} Genus on Hyper-Kahler Manifolds
Abstract
The group SL(2) acts on the space of cohomology groups of any hyper-Kahler manifold X. The \chi_{y} genus of a hyper-Kahler X is shown to have a geometric interpretation as the super trace of an element of SL(2). As a by product one learns that the generalized Casson invariant for a mapping torus is essentially the \chi_{y} genus.