Index formula for Hamiltonian loop group spaces

2021/06/07 by Loizides, Yiannis
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Symplectic Geometry (math.SG)

paper · doi:10.48550/arxiv.2106.03813

Abstract

We study K-theory classes of Hamiltonian loop group spaces represented by admissible Fredholm complexes. We prove various equivariant index formulae in this context. In a sequel to this article we show that, when specialized to a family of non-local elliptic boundary value problems over the moduli space of framed flat connections on a surface, one obtains a gauge theory analogue of the Teleman-Woodward index formula.

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