Skip to main content
Skip to main menu Skip to spotlight region Skip to secondary region Skip to UGA region Skip to Tertiary region Skip to Quaternary region Skip to unit footer

Slideshow

Topology Joint Seminar: Christine Ruey Shan Lee (University of South Alabama)

Christine Ruey Shan Lee
Boyd Room 304

A surface construction for colored Khovanov homology



Colored Khovanov homology is a categorification of the colored Jones polynomial. To each integer n ≥ 2 and a diagram D of a link, it assigns a bigraded chain complex. The graded Euler characteristic of the homology groups gives the nth colored Jones polynomial. It has typically been difficult to extract topological information from colored Khovanov homology due to its dependence on the combinatorics of link diagrams. We will give a construction of colored Khovanov homology of a knot in terms of embedded surfaces in the complement to more intrinsically motivate it using topology, and we will discuss potential applications. This work draws inspiration from Bar-Natan’s formulation of Khovanov homology and the Strong Slope Conjecture by Garoufalidis and Kalfagianni-Tran relating the colored Jones polynomial to topology of essential surfaces in the knot complement.

Support us

We appreciate your financial support. Your gift is important to us and helps support critical opportunities for students and faculty alike, including lectures, travel support, and any number of educational events that augment the classroom experience. Click here to learn more about giving.

Every dollar given has a direct impact upon our students and faculty.