Self-Linking for Legendrian Knots


Beasley, C. (2017). Self-Linking for Legendrian Knots. Perimeter Institute. https://pirsa.org/17020093


Beasley, Chris. Self-Linking for Legendrian Knots. Perimeter Institute, Feb. 24, 2017, https://pirsa.org/17020093


          @misc{ pirsa_17020093,
            doi = {10.48660/17020093},
            url = {https://pirsa.org/17020093},
            author = {Beasley, Chris},
            keywords = {Mathematical physics},
            language = {en},
            title = {Self-Linking for Legendrian Knots},
            publisher = {Perimeter Institute},
            year = {2017},
            month = {feb},
            note = {PIRSA:17020093 see, \url{https://pirsa.org}}

Chris Beasley Northeastern University


The Feynman diagram expansion for a Wilson loop observable in Chern-Simons gauge theory generates an infinite series of topological invariants for framed knots.  In this talk, I will describe a new perturbative formalism which conjecturally generates the same invariants for Legendrian knots in the standard contact R^3.  The formalism includes a `perturbative' localization principle which drastically simplifies the structure of calculations.  As time permits, I will provide some examples and applications.  This talk is based upon joint work with Brendan McLellan and Ruoran Zhang.