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The Homflypt skein module of L(p, 1): The braid approach.
by
Ioannis Diamantis
National Technical University of Athens
Coauthors: Sofia Lambropoulou, Jozef Przytycki
We represent links/braids in L(p, 1) by mixed links/braids in S3. The mixed braids are elements of the Artin Braid groups of type B, B1, n. We then give the analogue of Markov's Theorem in L(p, 1) in terms of braid equivalence in ∪n∞B1, n. The braid groups B1, n are represented in the generalized B-type Hecke algebras H1, n(q), on which a unique Markov trace has been constructed by Lambropoulou. We then give a new basis, Λ, for the Homflypt skein module of the solid torus, which was conjectured by Przytycki.
The new basis Λ is appropriate for computing the Homflypt skein module of the lens spaces, since the handle-slide moves are best described in terms of the basis Λ. Then, for computing the Homflypt skein module of L(p, 1) we solve an infinite system of equations resulting from the handle-slide moves. This system consists in finite self-contained subsystems.
Date received: December 1, 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-13.