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

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

2008-08-30

arxiv.org/abs/0809.0033v2

Mathematics

Group Theory

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

Scientific paper

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.

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