Topology Atlas | Conferences

Conference on Knot Theory and Its Applications to Physics and Quantum Computing; 60th birthday of Jozef H. Przytycki
January 6-9, 2015
University of Texas at Dallas
Richardson, TX, USA

Organizers
Mieczyslaw K. Dabkowski (UTD) Tobias Hagge (UTD) Valentina S. Harizanov (GWU) Viswanath Ramakrishna (UTD) Radmila Sazdanovic (NCSU) Adam S. Sikora (SUNYUB)

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Framed Cord Algebra Invariant of Knots in S1 ×S2
by
Xingshan Cui
University of California Santa Barbara
Coauthors: Zhenghan Wang

We generalize Ng's two-variable algebraic/combinatorial 0-th framed knot contact homology for framed oriented knots in S3 to knots in S1 ×S2, and prove that the resulting knot invariant is the same as the framed cord algebra of knots. Actually, our cord algebra has an extra variable, which potentially corresponds to the third variable in Ng's three-variable knot contact homology. Our main tool is Lin's generalization of the Markov theorem for braids in S3 to braids in S1 ×S2. We conjecture that our framed cord algebras are always finitely generated for non-local knots.

Date received: December 4, 2014

Copyright © 2014 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # cbjz-35.