
## 2. Topology of the moduli of Higgs bundles

1.     The topology of the moduli of Higgs bundles is only really “well-known” using Morse theoretic techniques for low ranks (rank $>4$ is where these techniques fall apart). We know many things (e.g. about Betti/Hodge numbers) through motivic/point counting methods, but it would be nice to have a concrete Morse theoretic explanation as well.

#### Problem 2.1.

Establish Morse theoretic approach to the study of the topology of Hitchin moduli spaces in high rank. In particular, find a geometric reason for the independence of the Poincaré polynomial on the degree (without appealing to the character variety).

Cite this as: AimPL: Singular geometry and Higgs bundles in string theory, available at http://aimpl.org/singularhiggs.