Ring groups and wickets
Tara Brendle (Glasgow)
Wednesday 24th September, 2008 16:00-17:00 214
We interpret the Hilden subgroup of the mapping class group of a surface in terms of motions of "wickets" in upper-half space. This group can also be viewed as a subgroup of a braid group. We will also use the wicket viewpoint to relate Hilden's group to the "ring-group," or the group of motions of circles in 3-space. Further, we will discuss a K(pi,1)-space for the wicket group as well as some related spaces among which we show certain homotopy equivalences. Among other applications, our methods give finite presentations for several related groups. This is joint work with Allen Hatcher.