The Automorphism Equivariant Hitchin Index
Organizers
Speaker
William Elbæk Mistegård
Time
Saturday, April 26, 2025 2:00 PM - 3:30 PM
Venue
A3-2a-302
Online
Zoom 482 240 1589
(BIMSA)
Abstract
Let T be the one-dimensional complex torus. We consider the action of an automorphism f of a Riemann surface X on the cohomology of the T-equivariant determinant line bundle over the moduli space M of rank two Higgs bundles on X with fixed determinant of odd degree. We define and study the automorphism equivariant Hitchin index. We prove a formula for it in terms of cohomological pairings of canonical T-equivariant classes of certain moduli spaces of parabolic Higgs bundles over the quotient Riemann surface.
The study of the automorphism equivariant Hitchin index is motivated by complex quantum Chern-Simons theory and non-abelian Hodge theory. Further, this index is a generalization of the Witten-Reshetikhin-Turaev quantum invariant of the three-manifold Y obtained as the mapping torus of the automorphism f. This project is based on joint work with J. E. Andersen and G. Ayuso.
The study of the automorphism equivariant Hitchin index is motivated by complex quantum Chern-Simons theory and non-abelian Hodge theory. Further, this index is a generalization of the Witten-Reshetikhin-Turaev quantum invariant of the three-manifold Y obtained as the mapping torus of the automorphism f. This project is based on joint work with J. E. Andersen and G. Ayuso.