Hello Topologists and Friends,
We are happy to Alex Zupan speaking this week, on Thursday at 3:30 in MSCS 514.
Title: The bridge number of high distance tangle sums
Abstract: A bridge sphere for a knot K in the 3-sphere cuts K into two
collections of unknotted arcs, and the bridge number of K is the
minimum number of arcs in such a decomposition. The behavior of
bridge number under taking connected sums is well-understood. On the
other hand, it is difficult to predict the bridge number of a knot
expressed as the sum of two arbitrary tangles. We will show the
bridge number of the sum of two sufficiently complicated tangles,
measured in terms of distances in the curve complex, behaves as
expected. This is joint work with Ryan Blair.
