  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 $F(T)$.
