Horizontal configurations of points in link complements

2005/09/07 by Daan Krammer
Mathematics · #math.GT #msc:57M25 #msc:57M27 #msc:55N25

paper · pdf

published as in Proc. European Congress Math. 2004, EMS (2005), 233--245 · 14 pages, 5 figures, uses pstricks

arxiv created 2005/09/07 · arxiv updated 2009/12/01

Abstract

For any tangle T (up to isotopy) and integer k≥ 1 we construct a group F(T) (up to isomorphism). It is the fundamental group of the configuration space of k points in a horizontal plane avoiding the tangle, provided the tangle is in what we call Heegaard position. This is analogous to the first half of Lawrence's homology construction of braid group representations. We briefly discuss the second half: homology groups of F(T).

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