Boston Graduate Topology Seminar

Boston College Meeting

Saturday, April 27, 9:00AM-12:15PM

Math Department, Maloney Hall, Room 560

Speakers:

9:30-10:15: Jen Hom (Georgia Tech)

Title: Concordance homomorphisms from knot Floer homology

Abstract: The knot concordance group consists of knots in the 3-sphere modulo an equivalence relation called concordance, with the operation induced by connected sum. We will define some new concordance homomorphisms coming from knot Floer homology, relate them to previously defined homomorphisms, and discuss some applications. This is joint work with I. Dai, M. Stoffregen, and L. Truong.

10:30-11:15: Chris Gerig (Harvard)

Title: Near-symplectic forms and the smooth Poincaré conjecture

Abstract: Most closed 4-manifolds do not admit symplectic forms. But most admit "near-symplectic forms", certain closed 2-forms which are symplectic outside of a collection of circles. This provides a gateway from the symplectic world to the non-symplectic world. I will first sketch an application, a geometric interpretation of the Seiberg-Witten invariants in terms of J-holomorphic curves that are compatible with the near-symplectic form. Although the SW invariants don't apply to (potentially exotic) 4-spheres, nor do these spheres admit near-symplectic forms (because the 4-sphere has trivial 2nd de Rham cohomology), there is still a way to bring in near-symplectic techniques. I will describe my failed attempt at building invariants of such spheres.

11:30-12:15: Zhenkun Li (MIT)

Title: Gradings on the sutured monopole Floer homology

Abstract: Give a balanced sutured manifold M and a properly embedded surface S in M, we can construct a grading associated to S on the sutured monopole Floer homology of M. This grading, however, does not only depends on the isotopy class of S, but also depends on the intersection of S with the suture. Under some circumstances, we could prove a formula relating different gradings associated to surfaces which are isotopic but have different intersections with the suture. We will discuss two applications of this formula. The first is to compute the sutured monopole Floer homology of a solid torus with any sutures. The second is to construct a minus version of monopole knot Floer homology, with an Alexander-grading and a U of degree -1.

Location & Parking:

The Math Department is located on the fifth floor of Maloney Hall (shown on some campus maps as 21 Campanella Way), near the center of the main campus (shown in red on the map below). It is adjacent to the Commonwealth Garage. See this for more directions (including Public Transportation information) for getting to campus.

Visitor parking is available in the Commonwealth Garage or the Beacon Street Garage.