Betti numbers of the moduli space of rank 3 parabolic Higgs bundles

Abstract

We compute the Betti numbers of the moduli space of rank 3 parabolic Higgs bundles, using Morse theory. A key point is that certain critical submanifolds of the Morse function can be identified with moduli spaces of parabolic triples. These moduli spaces come in families depending on a real parameter and we study their variation with this parameter.

78 pages. Extended version. Added a section with the fixed determinant case. To appear in Memoirs of the AMS

References in corpus (2)

• Mirror symmetry, Langlands duality, and the Hitchin system
• Examples of mirror partners arising from integrable systems

Cited by in corpus (3)

• Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
• From $S^1$-fixed points to $\mathcal{W}$-algebra representations
• On the motives of moduli of parabolic chains and parabolic Higgs bundles