Groups possessing only indiscrete embeddings in SL(2,C)

2012/10/09 by J. O. Button, Button, J. O.
Mathematics · #Advanced Combinatorial Mathematics #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #math.GT

paper · pdf · doi:10.48550/arxiv.1210.2691

Minor changes and updates

openalex publication_date 2012/10/09 · arxiv created 2012/11/26 · arxiv updated 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give results on when a finitely generated group has only indiscrete embeddings in SL(2,C), with particular reference to 3-manifold groups. For instance if we glue two copies of the figure 8 knot along its torus boundary then the fundamental group of the resulting closed 3-manifold sometimes embeds in SL(2,C) and sometimes does not, depending on the identification. We also give another quick counterexample to Minsky's simple loop question.

Citations

• The Free Product of Two Groups with a Malnormal Amalgamated Subgroup

Related

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• 3-manifolds with more than one abelian embedding
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