The density of Lawrence-Krammer and non-conjugate braid representations of links

2008/08/30 by A. Stoimenow, Alexander Stoimenow, Stoimenow, Alexander
Mathematics · #11E39 #20F36 #22E10 #32M05 #57M25 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.GR #math.GT #msc:11E39 #msc:20F36 #msc:22E10 #msc:32M05 #msc:57M25

paper · pdf · doi:10.48550/arxiv.0809.0033

18 pages, 1 figure; rev 30 Jun 09: changed Lemma 4, expanded Sec. 9 and fixed pf. of Theorem 2

openalex publication_date 2008/08/30 · arxiv created 2009/06/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We use some Lie group theory and Budney's unitarization of the Lawrence-Krammer representation, to prove that for generic parameters of definite form the image of the representation (also on certain types of subgroups) is dense in the unitary group. This implies that, except possibly for closures of full-twist braids, all links have infinitely many conjugacy classes of braid representations on any non-minimal number of (and at least 4) strands.

Citations

• ON THE IMAGE OF THE LAWRENCE–KRAMMER REPRESENTATION

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