The L-space conjecture has been in the news a lot lately. It predicts a surprising relationship between the algebraic, geometric, and Floer-homological properties of a 3--manifold Y. In particular, it predicts exactly which 3-manifolds admit a ``taut foliation". In this talk, I'll discuss some of my past and forthcoming work investigating these connections. In particular, I'll discuss a strategy for building taut foliations manifolds obtained by Dehn surgery along knots realized as closures of ``positive braids". As an application, I will show how taut foliations can be used to obstruct positivity for cable knots. All are welcome; no background in foliation or Floer homology theories will be assumed.
https://bccte.zoom.us/j/91883463721
Meeting ID: 918 8346 3721
Computing, understanding the behavior of concordance invariants obtained from knot Floer homology theories is quite central to the study of the concordance group and low-dimensional topology in general. In this talk, I will describe the method that allows us to compute the concordance invariant epsilon using combinatorial knot Floer homology and talk about some computational results. This is a joint work with S. Dey.
Please Note: Knots/links associated to overtwisted contact structures have been less explored. There are two types of knots/links in overtwisted contact manifolds, namely loose and non-loose. In this talk, I will start with an overview of these knots and then discuss some of my recent work involving these knots and links. Specifically, I will talk about a coarse classification result of loose, null-homologous Legendrian and transverse links . Next relating them with open book decompositions, I will show that coarse equivalence class of loose null-homologous Legendrian links has support genus zero. I will end with some interesting open questions.
The smallest volume cusped hyperbolic 3-manifolds, the figure-eight knot complement and its sister, contain many immersed but no embedded closed totally geodesic surfaces. In this talk we discuss the existence or lack thereof of codimension-1 closed embedded totally geodesic submanifolds in minimal volume cusped hyperbolic 4-manifolds. This talk is based on joint work with Alan Reid.
A cobordism between 3-manifolds is ribbon if it is built from handles of index no greater than 2. Such cobordisms arise naturally from several different topological and geometric contexts. In this talk, we discuss these objects and present a few obstructions to their existence, from Thurston geometries, character varieties, and instanton and Heegaard Floer homologies. This is joint work with Aliakbar Daemi, Tye Lidman, and Mike Wong.
Given a contact structure on a bordered 3-manifold, we describe an invariant which takes values in the bordered sutured Floer homology of the manifold. This invariant satisfies a nice gluing formula, and recovers the Oszvath-Szabo contact class in Heegaard Floer homology. This is joint work with Alishahi, Foldvari, Hendricks, Licata, and Vertesi.
Zoom info:
Meeting ID: 980 3103 5804
Passcode: 196398
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