ON THE KAUFFMAN BRACKET SKEIN MODULE OF SURGERY ON A (2, 2b) TORUS LINK
نویسنده
چکیده
We show that the Kauffman bracket skein modules of certain manifolds obtained from integral surgery on a (2, 2b) torus link are finitely generated, and list the generators for select examples.
منابع مشابه
On the Kauffman Skein Modules
Abstract. Let k be a subring of the field of rational functions in α, s which contains α, s. Let M be a compact oriented 3-manifold, and let K(M) denote the Kauffman skein module of M over k. Then K(M) is the free k-module generated by isotopy classes of framed links in M modulo the Kauffman skein relations. In the case of k = Q(α, s), the field of rational functions in α, s, we give a basis fo...
متن کاملTraces on the Skein Algebra of the Torus
For a surface F , the Kauffman bracket skein module of F × [0, 1], denoted K(F ), admits a natural multiplication which makes it an algebra. When specialized at a complex number t, nonzero and not a root of unity, we have Kt(F ), a vector space over C. In this paper, we will use the product-to-sum formula of Frohman and Gelca to show that the vector space Kt(T ) has five distinct traces. One tr...
متن کاملFundamentals of Kauffman bracket skein modules
Skein modules are the main objects of an algebraic topology based on knots (or position). In the same spirit as Leibniz we would call our approach algebra situs. When looking at the panorama of skein modules1, we see, past the rolling hills of homologies and homotopies, distant mountains the Kauffman bracket skein module, and farther off in the distance skein modules based on other quantum inva...
متن کاملOn the Kauffman Bracket Skein Module of the Quaternionic Manifold
We use recoupling theory to study the Kauffman bracket skein module of the quaternionic manifold over Z[A ±1 ] localized by inverting all the cyclotomic polynomials. We prove that the skein module is spanned by five elements. Using the quantum invariants of these skein elements and the Z 2-homology of the manifold, we determine that they are linearly independent.
متن کاملThe Skein Module of Two-bridge Links
We calculate the Kauffman bracket skein module (KBSM) of the complement of all two-bridge links. For a two-bridge link, we show that the KBSM of its complement is free over the ring C[t] and when reducing t = −1, it is isomorphic to the ring of regular functions on the character variety of the link group.
متن کامل