working topology seminar (spring 2017)

     

Topic: Khovanov homotopy type.  Khovanov homology is an invariant of links which categorifies the 
classical Jones polynomial.  This invariant has appeared in a number of contexts, including a combinatorial proof of the Milnor conjecture on torus knots, and has connections with many fields like representation theory, topological quantum field theory, and gauge theory.  This semester we will continue where we left off in the fall in trying to understand a homotopical construction of the Khovanov theory which contains even more information, such as in its Steenrod operations.

Sources: Original paper , Alternate version we will follow, Michael Abel's notes from a talk by Robert Lipshitz
                 
 Time/Location: 1:30-2:30 Thursday/SAS 4201

Organizers: Tye Lidman and Radmila Sazdanovic

Schedule:       
               
        Review of  flow categories - Michael (1/19)
        The cube  flow category - Claire (1/26)                           
        Cubical flow categories - Dmitry (2/2)  
        Cubical neat embeddings - Alex (2/9)
        Cubical realization - Dan (2/16)
        Defining the Khovanov spectrum - Tye (2/23)
        Some examples - Orsola (3/2)
        Cubical flow categories and Burnside category - Victor (3/23)
        Realizations coming from the Burnside category - Dmitry (4/6)   
        Homotopy colimits, products, and the Burnside category - Michael (4/13)                                                                 Concordance  and the four-ball genus - Tye (4/20)   
        Four-ball genus from the Khovanov spectrum - Alex (4/27)