Horizontal configurations of points in link complements

Details Horizontal configurations of points in link complements Horizontal configurations of points in link complements

2005-09-07

arxiv.org/abs/math/0509158v1

in Proc. European Congress Math. 2004, EMS (2005), 233--245

Mathematics

Geometric Topology

14 pages, 5 figures, uses pstricks

Scientific paper

For any tangle $T$ (up to isotopy) and integer $k\geq 1$ 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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