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arXiv:math/0506444 [math.AG]AbstractReferencesReviewsResources

Homotopy groups of moduli spaces of representations

Steven B. Bradlow, Oscar Garcia-Prada, Peter B. Gothen

Published 2005-06-22, updated 2007-06-14Version 4

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.

Comments: 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
Journal: Topology 47 (2008), 203-224
Categories: math.AG, math.DG
Subjects: 14H60, 57R57, 58D29
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