By J. Scott Carter, Seiichi Kamada, Louis H. Kauffman, Akio Kawauchi, Toshitake Kohno
This quantity gathers the contributions from the foreign convention "Intelligence of Low Dimensional Topology 2006," which happened in Hiroshima in 2006. the purpose of this quantity is to advertise learn in low dimensional topology with the focal point on knot conception and similar themes. The papers contain finished stories and a few newest effects.
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Extra resources for Intelligence of low dimensional topology 2006: Hiroshima, Japan, 22-26 July 2006
1. March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 33 + 6 Fig. 7. 6 61 60 6: AS and IHX relations, where ⊕ in TX means a positive half twist. 1. 1. We will show the ‘if’ part. Let Ta , Tb , Tb , Tc , Tc and Td be claspers as illustrated in Figure 8, and let T x (x = a, b, c, d) be claspers obtained from Tx by adding a half-twist on an edge. Recall that string links have a natural monoid structure arising from composition. Let L be a 2-string link. 4, L is C2 -equivalent to the product of µL (12) copies A if µL (12) ≥ 0 or −µL (12) copies A−1 if µL (12) < 0, where A is a string link obtained from the trivial string link 12 by surgery along Ta , and A−1 is obtained from 12 by surgery along T a .
Math. de France, Ast´erisque 107-108 (1983) 87–161. 2. J. Birman and W. Menasco, Studying knots via braids III: Classifying knots which are closed 3 braids, Paciﬁc J. Math. 161 (1993) 25–113.
1, we have MN (L) = 2 × h(R) = 2. Note that L has a Seifert surface R such that h(R) = 2. March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 40 Fig. 4. α1 α2 Fig. 5. 4. Connected sum The behavior of the handle number under a Murasugi sum has been studied in  and . 1. Let K1 K2 be a connected sum of K1 and K2 . Then, MN (K1 K2 ) ≤ MN (K1 ) + MN (K2 ). However the study of the behavior of the Morse-Novikov number under a connected sum is not complete, that is, the next natural question is still open as far as I know.
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