Boston Graduate Topology Seminar
Saturday, October 19, 9:30AM-12:15PM
Math Department, 4th Floor Lecture Room (Building 2, Room 449)
9:30-10:15: Irving Dai (MIT)
Title: Local equivalence and cobordism questions
Abstract: Heegaard Floer theory has proven to be a useful tool for studying cobordisms between 3-manifolds. We give a brief introduction to the notion of local equivalence, which is an algebraic way of organizing some of this Floer-theoretic information. We go over some applications to the homology cobordism group (joint with Matt Stoffregen, Jennifer Hom, and Linh Truong), as well as some newer results involving corks (joint with Abhishek Mallick).
10:30-11:15: Eylem Yildiz (Harvard)
Title: Exotic Stein manifolds and invertible knot concordances in S^1 x S^2.
Abstract: We use 4-dimensional handlebody technics to show that "All the knots in S^1 x S^2, which are homotopic to S^1 x pt, are invertibly concordant to S^1 x pt " relative to the boundary. By using this and the "roping" techniques we will demonstrate how to construct exotic contractible Stein manifold pairs, as well as exotic homotopy S^1 x B^3 pairs, which are Stein. Our construction involves finding "special" contractible Stein manifolds with high Thurston-Bennequin numbers, and then roping them to given corks and anticorks. Our exotic Stein manifold pairs have single 2-handles, which provides a solution to Problem 1.16 of the Kirby’s problem list. This is a joint work with Selman Akbulut.
11:30-12:15: Langte Ma (Brandeis)
Title: Gluing and surgery for Casson-Seiberg-Witten invariants of integral homology S^1 x S^3
Abstract: Given an integral homology S^1 x S^3, the Casson-Seiberg-Witten invariant λ_SW was introduced by Mrowka-Ruberman-Saveliev as a 4-dimensional analogue of Casson’s invariant. In this talk I will discuss how λ_SW changes under topological operations corresponding to the formulae for Casson’s invariant under surgery, connected-summing, and knot-splicing.