String topology studies various algebraic structures given by intersecting loops in a manifold, as well as those on the Hochschild chains or homology of an algebra. In this preparatory talk, we survey a collection of such structures and their relationships with one another.
A discussion of Khovanov-Lee homology, how to extract some invariants of braid closures from the homology theory, and motivation for studying both the homology theory and the invariants.
In the first talk I will introduce the main constructions, many of which are classical, from scratch. This part will be introductory and accessible to a general audience with a basic knowledge of topology. This introduction will also serve as preparation for the main talk in which I will outline the proof and discuss some applications.
I will discuss the orderability of the fundamental groups of knot complements including known results, a useful technique using some ideas of Baumslag, and some interesting questions that have recently arisen from this study.
I’ll try and give some background on the definition of knot Floer homology, and perhaps also bordered Heegaard Floer homology if time permits.
Heegaard Floer homology gives a powerful invariant of closed 3-manifolds. It is always computable in the purely combinatorial sense, but usually computing it needs a very hard work. However, for certain graph 3-manifolds, its minus-flavored Heegaard Floer homology can be easily computed in terms of lattice homology, due to Nemethi. I plan to give the basic definitions and constructions of Heegaard Floer theory and lattice homology, as well as the isomorphism between those two objects.
Georgia Institute of Technology
North Avenue, Atlanta, GA 30332
Phone: 404-894-2000
