63rd Cascade Topology Seminar

The relationship between mapping class groups of surfaces and low-dimensional topology has long been a fruitful one. From Thurston's characterization of geometric structures on mapping tori in terms of the Nielsen-Thurston type of the mapping class of a torus, to orita's result showing all homology 3-spheres arise in a certain way that is related to the Torelli subgroup of the mapping class group, to the recent resolution of Powell's conjecture for genus-3 splittings of the three-sphere by Freedman and Scharlemann (for a few examples among many), mapping class groups have been an extremely useful tool in 3-manifold topology.

Via surface bundles, results of Margalit-Baykur, Akhmedov, Morita, and Endo (to name only a few) have related algebraic properties of mapping class groups to topological properties of 4-manifolds. Combined with this, the recent introduction of trisections of 4-manifolds by Gay and Kirby has opened up an exciting new connection between 4-manifold topology and mapping class groups. This connection is already proving to be fruitful, both for understanding the topology of 4-manifold trisections, and for creating new and interesting research directions in mapping class groups.

The theme of this conference will be low-dimensional topology and the connections with mapping class groups and related topics in geometric group theory. The goal of the seminar is to highlight connections and commonalities between the fields and foster new collaborations between mathematicians based inn the Midwest and Eastern provinces, and those of the traditional Pacific northwest.