Representations of surface groups in the projective general linear group

André Oliveira

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arXiv · 0901.2314

Representations of surface groups in the projective general linear group

André Oliveira

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Abstract

Given a closed, oriented surface X of genus g>1, and a semisimple Lie group G, let R_G be the moduli space of reductive representations of the fundamental group of X in G. We determine the number of connected components of R_PGL(n,R), for n>=4 even. In order to have a first division of connected components, we first classify real projective bundles over such a surface. Then we achieve our goal, using holomorphic methods through the theory of Higgs bundles over compact Riemann surfaces. We also show that the complement of the Hitchin component in R_SL(3,R) is homotopically equivalent to R_SO(3).

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André Oliveira. 2009-01-15. Representations of surface groups in the projective general linear group. https://arxiv.org/abs/0901.2314

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