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**Abstract.** I will construct the first poly-time-computable knot
polynomial since Alexander's (1928) by 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.

**Sources:** pensieve.