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Knot Theory: Fifty Years Since Fox and Milnor
June 2-5, 2008
Brandeis University
Waltham (Massachusetts), USA

Organizers
Tim D. Cochran, Stavros Garoufalidis, Cameron Gordon, Daniel Ruberman, Kent Orr.

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The concordance genus of knots
by
Charles Livingston
Indiana University

The concordance genus of a knot K, gc(K), is the minimal 3-genus of a knot in the concordance class of K. An elementary argument shows that g4(K) ≤ gc(K) ≤ g3(K), where g3 and g4 denote the 3-genus and 4-genus. Early examples demonstrated that the inequalities can be strict. In this talk I will describe bounds on gc(K) based on invariants from Levine's algebraic concordance group. For almost all low crossing knots these bounds are sufficient to determine gc(K). I will also describe techniques for dealing with examples for which gc(K) cannot be determined from the algebraic concordance class of K.

Date received: May 9, 2008

Copyright © 2008 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 # caxb-16.