# I Still don't Understand the Alexander Polynomial

Date:

Time:

2021 04 01

14:30 (GMT+0)

Speaker:

Dror Bar-Natan

Mathematical colloquium in BMSTU

As an algebraic knot theorist, I still don't understand the Alexander

polynomial. There are two conventions as for how to present tangle

theory in algebra: one may name the strands of a tangle, or one may name

their ends. The distinction might seem too minor to matter, yet it leads

to a completely different view of the set of tangles as an algebraic

structure. There are lovely formulas for the Alexander polynomial as

viewed from either perspective, and they even agree where they meet. But

the "strands" formulas know about strand doubling while the "ends" ones

don't, and the "ends" formulas know about skein relations while the

"strands" ones don't. There ought to be a common generalization, but I

don't know what it is.

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