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

Kim A. Froyshov

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arXiv · 1304.0936

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

Kim A. Froyshov

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Abstract

Given a finite, connected 2-complex $X$ such that $b_2(X)\le1$ 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 the first rational cohomology group of $X$ is non-zero.

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Kim A. Froyshov. 2013-04-03. On the existence of representations of finitely presented groups in compact Lie groups. https://arxiv.org/abs/1304.0936

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