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Exchange moves and braid representations of links

By Reiko Shinjo and Alexander Stoimenow

Abstract

We prove that under fairly general conditions an iterated exchange move gives infinitely many non-conjugate braids. As a consequence, every knot has infinitely many conjugacy classes of n-braid representations if and only if it has one admitting an exchange move.Comment: 25 pages, 17 figure

Topics: Mathematics - Geometric Topology, Primary 57M25, Secondary 20F36, 57M27
Year: 2011
OAI identifier: oai:arXiv.org:1103.2510
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