A Geometric Interpretation of the -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 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 y genus.
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