Link homology theories and ribbon concordances

Link Homology Theories from Symplectic Geometry

For each positive integer n, Khovanov and Rozansky constructed an invariant of links in the form of a doubly-graded cohomology theory whose Euler characteristic is the sl(n) link polynomial. We use Lagrangian Floer cohomology on some suitable affine varieties to build a similar series of link invariants, and we conjecture them to be equal to those of Khovanov and Rozansky after a collapse of th...

On Link Homology Theories from Extended Cobordisms

Abstract. This paper is devoted to the study of algebraic structures leading to link homology theories. The originally used structures of Frobenius algebra and/or TQFT are modified in two directions. First, we refine 2–dimensional cobordisms by taking into account their embedding into R. Secondly, we extend the underlying cobordism category to a 2–category, where the usual relations hold up to ...

Link homology and categorification

This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics. 2000 Mathematics Subject Classification: 57M25, 57Q45.

Generalized Homology Theories

Link homology and Frobenius extensions

We explain how rank two Frobenius extensions of commutative rings lead to link homology theories and discuss relations between these theories, Bar-Natan theories, equivariant cohomology and the Rasmussen invariant. AMS Subject Classification: 57M27 Frobenius systems. Suppose ι : R −→ A is an inclusion of commutative rings, and ι(1) = 1. The restriction functor Res : A−mod −→ R−mod has left and ...