Download Low-Dimensional Topology II: Graphs on Surfaces and Their by Sergei K. Lando, Alexander K. Zvonkin PDF

By Sergei K. Lando, Alexander K. Zvonkin

Graphs drawn on two-dimensional surfaces have continuously attracted researchers through their attractiveness and by way of the diversity of inauspicious inquiries to which they provide upward thrust. the idea of such embedded graphs, which lengthy appeared quite remoted, has witnessed the looks of solely unforeseen new purposes in contemporary many years, starting from Galois idea to quantum gravity versions, and has develop into a type of a spotlight of an enormous box of study. The booklet presents an available creation to this new area, together with such themes as coverings of Riemann surfaces, the Galois crew motion on embedded graphs (Grothendieck's conception of "dessins d'enfants"), the matrix imperative procedure, moduli areas of curves, the topology of meromorphic services, and combinatorial features of Vassiliev's knot invariants and, in an appendix through Don Zagier, using finite team illustration idea. The presentation is concrete all through, with a variety of figures, examples (including machine calculations) and workouts, and may entice either graduate scholars and researchers.

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During this quantity, that's devoted to H. Seifert, are papers in line with talks given on the Isle of Thorns convention on low dimensional topology held in 1982.

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2Cn ], Ci = 0. Here S(p, q) is a link if and only if the length n is odd. 3. The braid index of 2-bridge links Let L be an oriented 2-bridge knot or link. In 1991, K. Murasugi [9] determined the braid index of L, using Morton-Franks-Williams inequality [8, 4] and Yamada’s braiding algorithm [12]. 4 of P. 1 (Murasugi). Let L be a 2-bridge link S(p, q), where 0 < q < p and q is odd. Let [2C1,1 , 2C1,2 , . . , 2C1,k1 , −2C2,1 , −2C2,2 , . . , −2C2,k2 , . . , (−1)t−1 2Ct,1 , . . , (−1)t−1 2Ct,kt ] be the unique continued fraction for q/p, where Ci,j > 0 for all i, j.

M. Khovanov, Categorification of the Jones polynomial. Duke Math. J. 87 (1997), 409-480. March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 25 6. K. Murasugi. The Jones polynomials of periodic links. Pacific J. Math. 131 (1988) pp. 319-329. 7. P. Traczyk. 10101 has no period 7: A criterion for periodicity of links. Proc. Amer. Math. Soc. 108, pp. 845-846. 1990. 8. O. Viro, Khovanov homology, its definitions and ramifications. Fund. Math. 184 (2004), 317-342 March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in This page intentionally left blank ws-procs9x6 March 27, 2007 11:10 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 Intelligence of Low Dimensional Topology 2006 Eds.

1) MN (L) = 0 if and only if L is fibred. (2) MN (L) = 2 × min{m1 (f ) | f is moderate}. 2. Heegaard splitting for sutured manifolds and product decompositions We recall the definition of a sutured manifold ([1]). A sutured manifold (M, γ) is a compact oriented 3-dimensional manifold M together with a set γ(⊂ ∂M ) of mutually disjoint annuli A(γ) and tori T (γ). In this paper, we deal with the case of T (γ) = ∅. The core curve of a component of A(γ) is called a suture, and we denote by s(γ) the set of sutures.

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