Vol. 7, No. 4, 2014

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On a state model for the $\mathrm{SO}(2n)$ Kauffman polynomial

Carmen Caprau, David Heywood and Dionne Ibarra

Vol. 7 (2014), No. 4, 547–563
Abstract

François Jaeger presented the two-variable Kauffman polynomial of an unoriented link L as a weighted sum of HOMFLY-PT polynomials of oriented links associated with L. Murakami, Ohtsuki and Yamada (MOY) used planar graphs and a recursive evaluation of these graphs to construct a state model for the sl(n)-link invariant (a one-variable specialization of the HOMFLY-PT polynomial). We apply the MOY framework to Jaeger’s work, and construct a state summation model for the SO(2n) Kauffman polynomial.

Keywords
graphs, invariants for knots and links, Kauffman polynomial
Mathematical Subject Classification 2010
Primary: 57M27
Secondary: 57M27, 57M15
Milestones
Received: 10 April 2013
Revised: 24 October 2013
Accepted: 27 October 2013
Published: 31 May 2014

Communicated by Colin Adams
Authors
Carmen Caprau
Department of Mathematics
California State University, Fresno
5245 N. Backer Avenue M/S PB108
Fresno, CA 93740-8001
United States
David Heywood
Department of Mathematics
California State University, Fresno
5245 N. Backer Avenue M/S PB108
Fresno, CA 93740-8001
United States
Dionne Ibarra
Department of Mathematics
California State University, Fresno
5245 N. Backer Avenue M/S PB108
Fresno, CA 93740-8001
United States