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

Abstract

Given a finite, connected 2-complex X such that b 2 (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 b 2 (X) = 1 we assume G = SO(3) and that the cup product on H 1 (X; Q) is non-zero.