By Editors: J. S. Carter, S. Kamada, L. H. Kauffman, A. Kawauchi, and T. Kohno
This quantity gathers the contributions from the foreign convention "Intelligence of Low Dimensional Topology 2006," which came about in Hiroshima in 2006. the purpose of this quantity is to advertise examine in low dimensional topology with the point of interest on knot thought and comparable themes. The papers contain complete stories and a few newest effects.
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Additional resources for Intelligence of Low Dimensional Topology 2006 (Series on Knots and Everything)
42 (2005), 557–572. 6. M. Hirasawa and L. Rudolph, Constructions of Morse maps for knots and links, and upper bounds on the Morse-Novikov number, preprint. 7. T. Kanenobu, The augmentation subgroup of a pretzel link, Math. Sem. Notes Kobe Univ. 7 (1979), 363–384. 8. J. Milnor, Singular points of complex hypersurfaces, Annals of Mathematics Studies, No. ; University of Tokyo Press, Tokyo 1968. 9. A. Pajitnov, Closed orbits of gradient ﬂows and logarithms of non-abelian Witt vectors, Special issues dedicated to Daniel Quillen on the occasion of his sixtieth birthday, Part V.
A Morse map f : CL → S 1 is said to be minimal if for each i the number mi (f ) is minimal on the class of all regular maps homotopic to f . Under these notations, the following basic theorem is shown (). 1 (). There is a minimal Morse map satisfying: (1) m0 (f ) = m3 (f ) = 0; March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 36 (2) All critical values of the same index coincide; (3) f −1 (x) is a Seifert surface of L for any regular value x. 1 is said to be moderate.
See Fig. 2. ) be an arc properly embedded in M as illustrated in Fig. 2, and set M = M − IntN (α1 ∪ α2 ). Then we may March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 39 regarded (M , γ) as a sutured manifold such that M is homeomorphic to D2 × S 1 . By the product decomposition as in Fig. 1, we have (M , γ) is a product sutured manifold. 1. Since it is known that L is not ﬁbred, we have MN (L) = 2 × h(R) = 2. α1 R+(γ) γ γ R-(γ) s(γ) R-(γ) α2 Fig. 2. s(γ) D D s(γ) s(γ') M' M'' Fig.