# Boston Graduate Topology Seminar

### MIT Meeting

Saturday, September 24, 9:30AM-12:15PM

Math Department, 4th Floor Lecture Room (Building 2, Room 449)

**Speakers:**

**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.

**Location:**

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

**For Speakers:**

Your audience will comprise graduate students at all levels, with varied backgrounds in geometry and topology (though perhaps with a Floer-theoretic bias). As such, it is **vital** that you provide lots of context and motivation. Why is what you're talking about important? What are the interesting open questions in the field (learning about open problems can be very inspiring)? What are tractable problems for graduate students related to the main topic? Answering these kinds of questions leaves audience members more satisfied and interested, and with more valuable knowledge, than does rushing full-bore towards your main result. On a related note, sacrifice technical details if talking about them will lose the attention of large portions of the audience or obscure the main point or cause you to rush.

**Contact:**

Anyone interested in giving a talk or learning more about the seminar should contact John Baldwin at john.baldwin@bc.edu.

**Support:**

This seminar is partially supported by NSF CAREER Grant DMS-1454865.