Homotopy groups of moduli spaces of representations

Abstract

We calculate certain homotopy groups of the moduli spaces for representations of a compact oriented surface in the Lie groups GL(n,C) and U(p,q). Our approach relies on the interpretation of these representations in terms of Higgs bundles and uses Bott--Morse theory on the corresponding moduli spaces.

21 pages; v2: improved results for moduli of representations in GL(n,C), provided proof of Proposition 4.13 (4.12 of v1) correcting argument given in earlier paper, other minor corrections; v3: corrected Remark 4.6, other minor corrections; v4: corrected statements of Proposition 4.17 and Theorems 4.19 and 4.22 (former Theorems 4.18 and 4.20); to appear in Topology

References in corpus (5)

• Surface group representations in PU(p,q) and Higgs bundles
• Moduli spaces of holomorphic triples over compact Riemann surfaces
• Geometry of the moduli space of Higgs bundles
• Representations of surface groups in the general linear group
• Representations of the fundamental group of a closed oriented surface in Sp(4,R)

Cited by in corpus (16)

• Higgs bundles and surface group representations in the real symplectic group
• The topology of moduli spaces of free group representations
• Homotopy Groups of Free Group Character Varieties
• Stratifications on the Moduli Space of Higgs Bundles
• Covering spaces of character varieties
• SO(p,q)-Higgs bundles and higher Teichmüller components
• On moduli spaces of Hitchin pairs
• A general Cayley correspondence and higher Teichmüller spaces
• Character Varieties and the Moduli of Quiver Representations
• Studying Deformations of Fuchsian Representations with Higgs Bundles
• Differential geometry of moduli spaces of quiver bundles
• Fundamental Group of Moduli Spaces of Representations
• Bad Representations and Homotopy of Character Varieties
• The homotopy type of a once-suspended 6-manifold and its applications
• Non-orientable surfaces and electric-magnetic duality
• Homotopy types of gauge groups over Riemann surfaces