A Geometric Interpretation of the χ-y Genus on Hyper-Kahler Manifolds
George Thompson
Abstract
The group SL(2) acts on the space of cohomology groups of any hyper-Kahler manifold X. The χy 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 χy genus.
Create a lesson
Related papers
Towards the Global Torelli Theorem
Daniil Serebrennikov
Disjoint and nearly disjoint sums of matrix multiplication tensors and their centroids
Martin Kassabov, J. M. Landsberg, Victor Souza et al.
Proper moduli spaces of isolated non-normal singularities
Jiucheng Dai, Daniel Halpern-Leistner, Mingjun Sun et al.
Divisors in projective bundles over the projective line whose complement is affine space
Remy van Dobben de Bruyn
Numerical Godeaux Surfaces with many disjoint (-2)-curves and Applications
Yifan Chen, YongJoo Shin
Nash Loci
Luca Sodomaco, Julian Weigert