By J. R Young

Writer: London, Souter e-book date: 1833 matters: Calculus, fundamental Notes: this can be an OCR reprint. there's a number of typos or lacking textual content. There are not any illustrations or indexes. if you happen to purchase the final Books variation of this e-book you get loose trial entry to Million-Books.com the place you could make a choice from greater than 1000000 books at no cost. you can even preview the e-book there.

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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.