Tangles in a Pole Dance Studio: A Reading of Massuyeau, Alekseev, and Naef

Algebra, Topology and the Grothendieck-Teichmüller group, Les Diablerets, August 29 - September 2, 2022.

Abstract. I will report on joint work with Zsuzsanna Dancso, Tamara Hogan, Jessica Liu, and Nancy Scherich. Little of what we do is original, and much of it is simply a reading of Massuyeau's arXiv:1511.03974 and Alekseev and Naef's arXiv:1708.03119.

We study the pole-strand and strand-strand double filtration on the space of tangles in a pole dance studio (a punctured disk cross an interval), the corresponding homomorphic expansions, and a strand-only HOMFLY-PT relation. When the strands are transparent or nearly transparent to each other we recover and perhaps simplify substantial parts of the work of the aforementioned authors on expansions for the Goldman-Turaev Lie bi-algebra.

URL: http://drorbn.net/ld22.

Handout: PDS.html, PDS.pdf.

Talk Video. Also on SwissMap and on YouTube (different version).

Sources: pensieve.