Topology in Molecular Biology

116 C. Cerf and A. Stasiak

b (even)

a (even) -1 crossings

+1 crossings

nullification

b (even)

a +1 crossings

(odd)^

+1 crossings

nullification

b (odd)

a (even) -1 crossings

-1 crossings

nullification

a

b

b (odd)

a (odd)

b (odd)

a +1 crossings

(odd)

+1 crossings

nullification

b (odd)

a -1 crossings

(odd)

-1 crossings

nullification

a

b c d

e f g

Fig. 6.3.(a) A rational tangle with two rows, containingaandbcrossings, re-
spectively. Drawings (b), (c), and (d) show the nullification of the knot obtained
by the closure of the tangle in the casesaodd andbeven,aandbeven,aeven
andbodd, respectively. (e) In the caseaandbodd, the closure of the tangle gives
rise to a two-component link. Depending on the orientation chosen for the second
component, two different situations occur, shown in (f)and(g)