### Wicket Subgroups of Braid Groups (Allen Hatcher)

### Abstract:

This talk represents joint work with Tara Brendle. We show the space of
configurations of n disjoint semicircles (wickets) in upper half-space
meeting the boundary plane orthogonally in their endpoints is aspherical.
Its fundamental group W_n is a subgroup of the braid group on 2n strands,
and contains two copies of the braid group on n strands. There is a nice
presentation of W_n in terms of these two subgroups together with simple
twists of the wickets. The group W_n is closely related to the fundamental
group of the space of configurations of n disjoint circles in 3-space, the
so-called symmetric automorphism group of a free group.