Products of commutators in free groups and alternating knots of given genus
by
Alina Vdovina
Binghamton University

A Wicks form is a canonical form of a product of commutators in a free group F. The genus of a Wicks form w is the least positive integer g such that w is a product of g commutators in F. Wicks forms of genus g are closely related to the structure of alternating knots of genus g: every knot can be interpreted as a special word. This gives, for example, an asymptotic behaviour of the number of alternating knots up to a constant.

Date received: March 21, 2002

Copyright © 2002 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-88.