The Universal Approach to Link Homology Theory


Gad Naot

University of Toronto

November 13, 2006


Abstract: In this talk I will introduce my recent research, presenting the universal Khovanov link homology theory. This theory is developed using a topological formalism and has many computational and theoretical advantages. The universal theory answers questions regarding the precise amount of algebraic information held within the complex associated to a link. It also answers questions regarding the extraction of this information by giving full control over the various TQFTs (functors) applied to the complex (along with control over other gadgets such as the various spectral sequences related to these TQFTs). After an overview and some reminders I will introduce the major tools and ideas used in developing the universal theory (such as surface classification, genus generating operators, "delooping"  and "promotions"). Then I will present some of the advantages of such a theory, time permitting (more on the topic can be found at arXiv:GT/0603347).