Hi all,
We have many topology talks coming up in the next week. In addition to the Redbud conference over the weekend, Jeff Meier will speak in the usual Thursday 3:30pm timeslot, and Ken Baker will speak at 4:00pm next Monday. Both talks will be in MSCS 514. Titles and abstracts below.
Jeff Meier: Bridge trisections for knotted surfaces in $S^4$
Recently, Gay and Kirby introduced a new way of describing a 4--manifold called a \emph{trisection}, which involves decomposing the 4--manifold into three 4--dimensional handlebodies and serves as a 4--dimensional analogue to a Heegaard splitting of a 3--manifold. We adapt their approach to the setting of knotted surfaces in $S^4$; namely, we show that every such surface $\mathcal K$ admits a \emph{bridge trisection}, which is a decomposition of $(S^4,\mathcal K)$ into three pieces, each of which is a collection of trivial disks in $B^4$. A bridge trisection associates two complexity parameters to $\mathcal K$, giving a complexity measure analogous to the bridge number of a classical knot, and we give a classification of knotted surfaces with low bridge number. The theory gives rise to a new way to describe knotted surfaces in $S^4$ diagrammatically in terms of a triple of trivial (classical) tangle diagrams called a \emph{tri-plane diagram}. This is joint work with Alexander Zupan.
Ken baker: Unifying unexpected exceptional Dehn surgeries
In summer 2014, Dunfield-Hoffman-Licata produced examples of asymmetric, hyperbolic, 1-cusped 3-manifolds with pairs of lens space Dehn fillings through a search of the extended SnapPea census. Examinations of these examples with Hoffman and Licata lead us to coincidences with other work in progress that gives a simple holistic topological approach towards producing and extending many of these families. In this talk we'll explicitly describe our construction and discuss related applications of the technique.