Elsevier

Topology and its Applications

Volume 160, Issue 15, 15 September 2013, Pages 1987-2002
Topology and its Applications

On the existence of representations of finitely presented groups in compact Lie groups

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Abstract

Given a finite, connected 2-complex X such that b2(X)1 we establish two existence results for representations of the fundamental group of X into compact connected Lie groups G, with prescribed values on certain loops. If b2(X)=1 we assume G=SO(3) and that the cup product on H1(X;Q) is non-zero.

MSC

primary
57M07
secondary
57M20

Keywords

Finitely presented groups
Representations
Lie groups
3-Manifolds

Cited by (0)

1

Supported by the Danish National Research Foundation grant DNRF95 (Centre for Quantum Geometry of Moduli Spaces – QGM).