New York Journal of Mathematics
Volume 18 (2012) 337-351


Alissa S. Crans, Sam Nelson, and Aparna Sarkar

Enhancements of rack counting invariants via dynamical cocycles

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Published: May 22, 2012
Keywords: Dynamical cocycles, enhancements of counting invariants, cocycle invariants
Subject: 57M27, 57M25

We introduce the notion of N-reduced dynamical cocycles and use these objects to define enhancements of the rack counting invariant for classical and virtual knots and links. We provide examples to show that the new invariants are not determined by the rack counting invariant, the Jones polynomial or the generalized Alexander polynomial.

Author information

Alissa S. Crans:
Department of Mathematics, Loyola Marymount University, Los Angeles, CA 90045

Sam Nelson:
Department of Mathematics, Claremont McKenna College, Claremont, CA 91711

Aparna Sarkar:
Department of Mathematics, Pomona College, Claremont, CA 91711