The Homflypt skein module of a connected sum of 3–manifolds
نویسندگان
چکیده
منابع مشابه
The Homflypt Skein Module of a Connected Sum of 3-manifolds
Abstract. If M is a compact oriented 3-manifold, let S(M) denote the Homflypt skein module of M. We show that S(M1#M2) is isomorphic to S(M1)⊗ S(M2) modulo torsion. In fact, we show that S(M1#M2) is isomorphic to S(M1) ⊗ S(M2) if we are working over a certain localized ring. We show a similar result holds for relative skein modules. If M contains a separating 2-sphere, we give conditions under ...
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Let k be a subring of the field of rational functions in x, v, s which contains x, v, s. If M is an oriented 3-manifold, let S(M) denote the Homflypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Homflypt skein relations: (1) xL+ − xL− = (s − s)L0; (2) L with a positive twist = (xv)L; (3) L ⊔ O = ( v−v −1 s−s−1 )...
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This paper is a presentation, where we compute the HOMFLYPT Skein module of singular links in the 3-sphere. This calculation is based on some results previously proved by Rabenda and the author on Markov traces on singular Hecke algebras, as well as on classical techniques that allow to pass from the framework of Markov traces on Hecke algebras to the framework of HOMFLYPT Skein modules. Some o...
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Let k be a subring of the eld of rational functions in x; v; s which contains x 1 ; v 1 ; s 1. If M is an oriented 3-manifold, let S(M) denote the Hommypt skein module of M over k. This is the free k-module generated by isotopy classes of framed oriented links in M quotiented by the Hommypt skein relations: (1) x ?1 L + ? xL ? = (s ? s ?1)L 0 ; (2) L with a positive twist = (xv ?1)L; (3) L t O ...
متن کاملThe Kauffman Skein Module of the Connected Sum of 3-manifolds
Let k be an integral domain containing the invertible elements α, s and 1 s−s −1 . If M is an oriented 3-manifold, let K(M) denote the Kauffman skein module of M over k. Based on the work on Birman-Murakami-Wenzl algebra by Beliakova and Blanchet [2], we give an “idempotent-like” basis for the Kauffman skein module of handlebodies. Gilmer and Zhong [6] have studied the Homflypt skein modules of...
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ژورنال
عنوان ژورنال: Algebraic & Geometric Topology
سال: 2001
ISSN: 1472-2739,1472-2747
DOI: 10.2140/agt.2001.1.605