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A Geometric Interpretation of the χ-{y} Genus on Hyper-Kahler Manifolds

George Thompson
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Abstract

The group SL(2) acts on the space of cohomology groups of any hyper-Kahler manifold X. The χ_{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 χ_{y} genus.

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George Thompson. 1999-05-18. A Geometric Interpretation of the χ-{y} Genus on Hyper-Kahler Manifolds. https://doi.org/10.1007/s002200000230

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