By J Scott Carter, Seiichi Kamada, Louis H Kauffman, Akio Kawauchi, Toshitake Kohno

This quantity gathers the contributions from the overseas 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 conception and comparable themes. The papers comprise accomplished studies and a few newest effects.

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Ce cours de topologie a été dispensé en licence à l'Université de Rennes 1 de 1999 à 2002. Toutes les constructions permettant de parler de limite et de continuité sont d'abord dégagées, puis l'utilité de los angeles compacité pour ramener des problèmes de complexité infinie à l'étude d'un nombre fini de cas est explicitée.

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Could March 4, 2007 11:41 WSPC - Proceedings Trim Size: 9in x 6in ws-procs9x6 30 Fig. 2. The Hopf link with both components Whitehead doubled. this be true for links with a larger number of components? For a certain class of links, it is. A link L is called a boundary link if the components of L bound disjoint Seifert surfaces. Shibuya and the second author have shown that boundary links (with any number of components) are self C2 -equivalent to the trivial link [11]. However, whether the vanishing of the self C2 -invariant Milnor numbers implies that an arbitrary link is self C2 -trivial is not yet known.

The latter case happens between two blocks. Here, Ck may be 0. For example, 1849/10044 = [6, 2, 4, −6, −2, −6, 4] is modiﬁed to 1 + [−1, 4, −1, 0, −1, 2, −1, −6, +1, 0, +1, −4, +1, 4, −1]. Note that j Cj = B(L) − 1 + j (|Cj | − 1). According to such a modiﬁed continued fraction, we have a Conway diagram for L. See Figure 3 (left) depicting the example above. Each horizontal half twist corresponds to an inserted ±1, and the vertical twistings correspond to the entries Cj . The diagram carries a checker board Seifert surface F for L, which is of minimal genus.

S) = {cirles with + sign} − { circles with − sign }. Let i and j be two integers. We deﬁne C i (D) to be the free abelian group generated by all enhanced states with i(S) = i. Let C i,j (D) be the subgroup of C i (D) generated by enhanced states with j(S) = j. The Khovanov diﬀerential is deﬁned by: di,j : C i,j (D) −→ C i+1,j (D) S −→ (−1)t(S,S ) (S : S )S All states S’ where (S : S ) is • 1 if S and S diﬀer exactly at one crossing, call it v, where S has a +1 marker, S has a −1 marker, all the common circles in DS and DS have the same signs and around v, S and S are as in ﬁgure 2, • (S : S ) is zero otherwise and t(S, S ) is the number of −1 markers assigned to crossings in S labelled greater than v.