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arXiv:1304.0936 [math.GT]AbstractReferencesReviewsResources

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

Kim A. Froyshov

Published 2013-04-03, updated 2013-08-08Version 4

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.

Comments: 22 pages, to appear in `Topology and its Applications'. v2: The title was changed, reflecting the fact that Cor. 1.1 was already known. The old Theorem 1.5 was omitted, as it is easily proved using a result in the new appendix. v3: Only minor changes. v4: The proof of Prop. 2.1 was omitted, because the result was already known. Minor changes following referee's suggestions
Journal: Topology and its Applications 160 (2013) 1987-2002
Categories: math.GT, math.AT, math.GR
Subjects: 57M07, 57M20
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