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A Poly-Time Knot Polynomial Via Solvable Approximation

Massachusetts Institute of Technology, December 9, 2016

Abstract. Rozansky [Ro] and Overbay [Ov] described a spectacular knot polynomial that failed to attract the attention it deserved as the first poly-time-computable knot polynomial since Alexander's (1928) and (in my opinion) as the second most likely knot polynomial (after Alexander's) to carry topological information. With Roland van der Veen, I will explain how to compute the Rozansky polynomial using some new commutator-calculus techniques and a Lie algebra ${\mathfrak g}_1$ which is at the same time solvable and an approximation of the simple Lie algebra $sl_2$.

Handout: PPSA.html, PPSA.pdf, PPSA.png.

Talk Videos: Hour 1, Hour 2.

Sources: pensieve.