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Showing 1 to 4 of 4 for “"Kauffman Bracket"”.
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The Kauffman Bracket and Genus of Alternating Links
… there are three rules to help us finding the Kauffman bracket polynomial. Choosing knot’s orientation, then applying the Seifert algorithm to find the Euler characteristic and genus of its surface. Finally finding the relationship of the Kauffman bracket polynomial and the genus of the …
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Kauffman Bracket Skein Modules And The Quantum Torus
If M is a 3-manifold, the Kauffman bracket skein module is a vector space Kq (M ) functorially associated to M that depends on a parameter q ∈ C* . If F is a surface, then Kq (F x [0, 1]) is an algebra, and Kq (M ) is a module over Kq ((∂M ) x [0, 1]). One motivation for the definition is that if L …
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On conjectures related to character varieties of knots and Jones polynomials
It is well known that the Kauffman Bracket Skein Module of a knot complement K_q(S^3 \ K) is canonically a module over the Z_2-invariants of the quantum torus, A_q^{Z_2}, and this module determines the colored Jones polynomials J_n(K; q) of the knot K. Berest and Samuelson identified a conjecture …
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Knots, Skein Theory and q-Series
… of alternating links using the colored Kauffman skein relation. This gives a natural extension of a result by Kauffman, Murasugi, and Thistlethwaite regarding the highest and lowest coefficients of Jones polynomial of alternating links. Furthermore, we show that our approach gives a new …