A Geometric Interpretation of the \chi-{y} Genus on Hyper-Kahler Manifolds
Algebraic Geometry
2009-10-31 v1 High Energy Physics - Theory
Mathematical Physics
Differential Geometry
math.MP
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.
Keywords
Cite
@article{arxiv.math/9905102,
title = {A Geometric Interpretation of the \chi-{y} Genus on Hyper-Kahler Manifolds},
author = {George Thompson},
journal= {arXiv preprint arXiv:math/9905102},
year = {2009}
}