[Mdtop] Topology Seminar Thursday

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.