Dartmouth Topology Seminar
Fall 2018–Spring 2019
Fall 2018: Thursday 4-5 PM
Winter and Spring 2019: Thursday 2:30-3:30 PM
201 Kemeny Hall
Note: Special meeting times are marked in red.
Date Speaker Title
Apr. 18 Steven Boyer
Apr. 11 Alexander Dranishnikov
(University of Florida)
Apr. 4 Robert Low
(Coventry University)
Mar. 28 Akram Alishahi
Feb. 28 Joshua Sussan
Oct. 25 Bülent Tosun
(University of Alabama)
Contact surgeries, Symplectic Fillings and Lagrangian discs
Oct. 11 Samantha Allen
(Dartmouth College)
Nonorientable surfaces bounded by knots
Oct. 4 Shelly Harvey
(Rice University)
A non-discrete metric on the group of topologically slice knots
Sept. 20 Lev Tovstopyat-Nelip
(Boston College)
The transverse invariant and braid dynamics

April 18, 2019: Steven Boyer "TBA"


April 11, 2019: Alexander Dranishnikov "TBA"


April 4, 2019: Robert Low "TBA"


March 28, 2018: Akram Alishahi "TBA"


February 28, 2018: Joshua Sussan "TBA"


October 25, 2018: Bülent Tosun "Contact surgeries, Symplectic Fillings and Lagrangian discs"

Abstract:It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties are preserved under various types of contact surgeries. The case for the negative contact surgeries is fairly well understood. In this talk, we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically/Stein fillable for r in (0,1]. This is joint work with James Conway and John Etnyre.

October 11, 2018: Samantha Allen "Nonorientable surfaces bounded by knots"

Abstract: The nonorientable 4–genus of a knot K is the minimal first Betti number of a nonorientable surface in B^4 whose boundary is K. Finding the nonorientable 4–genus of a knot can be quite intractable; existing methods exploit the relationship between nonorientable genus and normal Euler number of the nonorientable surface. In this talk, I will give an overview of the interplay between the nonorientable genus and normal Euler number of nonorientable surfaces in B^4. I will define both of these invariants and discuss their computation. In particular, when fixing a knot K, we can ask what pairs of nonorientable genus and normal Euler number are realizable for a surface whose boundary is K. We will see that both classical invariants and Heegaard–Floer invariants can be used towards answering this question.

October 4, 2018: Shelly Harvey "A non-discrete metric on the group of topologically slice knots"

Abstract: Most of the 50-year history of the study of the set of smooth knot concordance classes, C, has focused on its structure as an abelian group. Tim Cochran and I took a different approach, namely we studied C as a metric space (with the slice genus metric) admitting many natural geometric operators. The goal was to give evidence that the knot concordance is a fractal space. However, both of these metrics are integer valued metrics and so induce the discrete topology. Subsequently, with Mark Powell, we defined a family of real valued metrics, called the q-grope metrics, that take values in the real numbers and showed that there are sequences of knots whose q-norms get arbitrarily small for q>1. However, for q>1, this metric vanishes on topologically slice knots (it is really a pseudo metric). In this talk, we define a new metric (called the tower metric) based on a new objects which we called positive and negative towers, using a combination of generalized handles and gropes. This is an interesting metric since it is related to the bipolar filtration, a filtration generalizing work of Gompf and Cochran. Using recent work of Cha and Kim on the non-triviality of the bipolar filtration of the group of topologically slice knots, we show that there are sequences of topologically slice knots whose q-norms get arbitrarily small but are never 0. This work is joint with Tim Cochran, Mark Powell, and Aru Ray.

September 20, 2018: Lev Tovstopyat-Nelip "The transverse invariant and braid dynamics"

Abstract: Let K be a link braided about an open book (B,p) supporting a contact manifold (Y,xi). K and B are naturally transverse links. We prove that the hat version of the transverse link invariant defined by Baldwin, Vela-Vick and Vertesi is non-zero for the union of K with B. As an application, we prove that the transverse invariant of any braid having fractional Dehn twist coefficient greater than one is non-zero. This generalizes a theorem of Plamenevskaya about classical braid closures.