Instantons and multibananas: Relating elliptic genus and cohomological Donaldson-Thomas theory

Abstract

In this article the cohomological Donaldson-Thomas theory of local multibanana threefolds is computed using Descombes' hyperbolic localisation formula. The resulting expression is precisely given by the elliptic genus of the moduli space of framed instanton sheaves. As part of the proof, an infinite-wedge-space trace formula is computed for the elliptic genus of the moduli space of framed instanton sheaves.