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Dror Bar-Natan:
Talks:
# I Still Don't Understand the Alexander Polynomial

### Bauman Moscow State Technical University Mathematical Colloquium,
April 1, 2021, Moscow 5:30PM / Toronto 10:30AM.

#### By web: JOIN
(Meeting ID: 948 341 6153, Password: 2SXtEz).

**Abstract.** 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.

**Handout:** AnG.pdf

**Annotated Slides:** AnG@.pdf

**Talk Video**. (Also @YouTube).

**Pensieve**.

**URL:** http://drorbn.net/mo21.