Index formula for Hamiltonian loop group spaces
Abstract
We study Ktheory 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 nonlocal elliptic boundary value problems over the moduli space of framed flat connections on a surface, one obtains a gauge theory analogue of the TelemanWoodward index formula.
 Publication:

arXiv eprints
 Pub Date:
 June 2021
 DOI:
 10.48550/arXiv.2106.03813
 arXiv:
 arXiv:2106.03813
 Bibcode:
 2021arXiv210603813L
 Keywords:

 Mathematics  Symplectic Geometry;
 Mathematics  Algebraic Geometry;
 Mathematics  KTheory and Homology
 EPrint:
 40 pages. The previous version has been divided into two parts