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

Kim A. Froyshov

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

Geometric Topology 2013-09-12 v4 Algebraic Topology Group Theory

Authors: Kim A. Froyshov

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.

Keywords

fundamental group compact lie groups finite presentation representation existence 2-complex rational cohomology cup product

Cite

@article{arxiv.1304.0936,
  title  = {On the existence of representations of finitely presented groups in compact Lie groups},
  author = {Kim A. Froyshov},
  journal= {arXiv preprint arXiv:1304.0936},
  year   = {2013}
}

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

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

Abstract

Keywords

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