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.
The Jumping Phenomenon of the Dimensions of Cohomology Groups of Tangent Sheaf
A geometric interpretation and a new proof of a relation by Cornalba and Harris
Geometric interpretation of valuated term (pre)orders
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