Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial

Dror Bar-Natan

Knots in Washington XXXIV; Categorification of Knots, Quantum Invariants and Quantum Computing
March 14-16, 2012
George Washington University
Washington, DC, USA

Organizers
Valentina Harizanov (GWU),Mark Kidwell (U.S. Naval Academy and GWU), Jozef H. Przytycki (GWU), Yongwu Rong (GWU), Radmila Sazdanovic (U.Penn), Alexander Shumakovitch (GWU), Hao Wu (GWU)

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Meta-Groups, Meta-Bicrossed-Products, and the Alexander Polynomial
by
Dror Bar-Natan
University of Toronto

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 üniversal finite type invariant of w-knots" and of an elusive üniversal finite type invariant of v-knots".

Date received: March 1, 2012