Abstract. A straightforward proposal for a group-theoretic invariant of knots fails if one really means groups, but works once generalized to meta-groups (to be defined). We will construct one complicated but elementary meta-group as a meta-bicrossed-product (to be defined), and explain how the resulting invariant is a not-yet-understood generalization of the Alexander polynomial, while at the same time being a specialization of a somewhat-understood "universal finite type invariant of w-knots" and of an elusive "universal finite type invariant of v-knots".
This will be an informal talk in the spirit of the talk I will be giving next week at Knots in Washington XXXIV.
Talk video. , Handout: beta.html, beta.pdf, beta.png, Sources: beta.zip, Pensieve: 2012-03.