Boston Graduate Topology Seminar

MIT Meeting
Saturday, September 24, 9:30AM-12:15PM
Math Department, 4th Floor Lecture Room (
Building 2, Room 449)


9:30-10:15: David Gay (UGA)

Title: How not to prove the smooth 4-dimensional Poincare conjecture

Abstract: This title is ripped off from Stallings' beautiful paper "How not to prove the Poincare conjecture", in which he reduces the 3-dimensional Poincare conjecture to certain group theoretic statements. I'll do the same in dimension 4, setting up a theory of "group trisections" whereby certain purely group theoretic objects are in one-to-one correspondence with diffeomorphism classes of smooth 4-manifolds.

10:30-11:15: Katherine Raoux (Brandeis)

Title: A generalization of the tau-invariant to rationally null-homologous knots

Abstract: Since it was introduced in 2004, the Ozsvath-Szabo tau-invariant has been a useful tool for studying genus and concordance of knots in the 3-sphere. Using Ni's construction of the Alexander grading for rationally null-homologous knots, I will show that one can define a collection of tau-invariants for any knot in a rational homology 3-sphere. In particular, these invariants are rational concordance invariants. Moreover, if K is a knot in the boundary of a negative definite four-manifold, the tau-invariants give a lower bound for the genus of any properly embedded surface with boundary K.

11:30-12:15: Sherry Gong (MIT)

Title: Marked link invariants

Abstract: We study the instanton spectral sequence associated to a link with a singular bundle and, in particular, related it to a version of Khovanov homology with such data, in the case of alternating links. We will also explore the binary dihedral representations of alternating links with such bundle data.

The Mathematics Department is located in Building 2. See Directions and Campus Map.