Wednesday, October 11, 2017 - 13:55 , Location: Skiles 006 , Justin Lanier , Georgia Tech , Organizer: Jennifer Hom
We will discuss the mapping class groupoid, how it is generated by handle slides, and how factoring in the mapping class groupoid can be used to compute Heegaard Floer homology. This talk is based on work by Lipshitz, Ozsvath, and Thurston.
Wednesday, October 4, 2017 - 13:55 , Location: Skiles 006 , Libby Taylor , Georgia Tech , Organizer: Jennifer Hom
Let K be a tame knot in S^3. Then the Alexander polynomial is knot invariant, which consists of a Laurent polynomial arising from the infinite cyclic cover of the knot complement. We will discuss the construction of the Alexander polynomial and, more generally, the Alexander invariant from a Seifert form on the knot. In addition, we will see some connections between the Alexander polynomial and other knot invariants, such as the genus and crossing number.
Wednesday, September 27, 2017 - 13:55 , Location: Skiles 006 , Anubhav Mukherjee , Georgia Tech , Organizer: Justin Lanier
Let S be an (n-1)-sphere smoothly embedded in a closed, orientable, smooth n-manifold M, and let the embedding be null-homotopic. We'll prove in the talk that, if S does not bound a ball, then M is a rational homology sphere, the fundamental group of both components of M\S are finite, and at least one of them is trivial. This talk is based on a paper of Daniel Ruberman.
Wednesday, September 20, 2017 - 13:55 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
The theory of braids has been very useful in the study of (classical) knot theory. One can hope that higher dimensional braids will play a similar role in higher dimensional knot theory. In this talk we will introduce the concept of braided embeddings of manifolds, and discuss some natural questions about them.
Wednesday, September 13, 2017 - 13:55 , Location: Skiles 006 , Hyun Ki Min , Georgia Tech , Organizer: Jennifer Hom
The Weeks manifold W is a closed orientable hyperbolic 3-manifold with the smallest volume. Understanding contact structures on hyperbolic 3-manifolds is one of problems in contact topology. Stipsicz previously showed that there are 4 non-isotopic tight contact structures on the Weeks manifold. In this talk, we will exhibit 7 non-isotopic tight contact structures on W with non-vanishing Ozsvath-Szabo invariants.
Wednesday, April 5, 2017 - 14:05 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Justin Lanier
Continuing from last time, we will discuss Hilden and Montesinos' result that every smooth closed oriented three manifold is a three fold branched cover over the three sphere, and also there is a representation by bands.
Wednesday, March 29, 2017 - 14:05 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Justin Lanier
In this series of talks we will show that every closed oriented three manifold is a branched cover over the three sphere, with some additional properties. In the first talk we will discuss some examples of branched coverings of surfaces and three manifolds, and a classical result of Alexander, which states that any closed oriented combinatorial manifold is always a branched cover over the sphere.