Horizontal Configurations of Points in Link Complements

  • Daan Krammer

    University of Warwick, Coventry, United Kingdom
Horizontal Configurations of Points in Link Complements cover
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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) .