Higgs bundles for the non-compact dual of the unitary group

TL;DR

This paper proves the connectedness of the moduli space of U*(2n)-Higgs bundles over a compact Riemann surface using Morse-theoretic methods, contributing to the understanding of Higgs bundle moduli spaces.

Contribution

It introduces Morse-theoretic techniques to establish the connectedness of the moduli space for U*(2n)-Higgs bundles, a non-compact dual of the unitary group.

Findings

Moduli space of U*(2n)-Higgs bundles is connected.

Morse theory is effective for studying Higgs bundle moduli.

Provides new insights into the topology of Higgs bundle moduli spaces.

Abstract

Using Morse-theoretic techniques, we show that the moduli space of U*(2n)-Higgs bundles over a compact Riemann surface is connected.