Knot theory is a rapidly developing field of research with many applications not only for
mathematics. The present volume, written by a well-known specialist, gives a complete …

We consider composite links obtained by bandings of another link. It is shown that if a
banding of a split link yields a composite knot then there is a decomposing sphere crossing …

We give some relationships of the Jones and Q polynomials between two links which are
related by a band surgery. Then we consider two applications: The first one is to an …

The connected-sum of a knot and its mirror image with orientation reversed is a ribbon knot.
Conversely, we show that if K 0 and K 1 are knots which are minimal with respect to ribbon …

The ribbon number $ r (K) $ of a ribbon knot $ K\subset S^ 3$ is the minimal number of
ribbon intersections contained in any ribbon disk bounded by $ K $. We find new lower …

On Nullification of Knots and Links Page 1 Western Kentucky University TopSCHOLAR®
Masters Theses & Specialist Projects Graduate School 5-2012 On Nullification of Knots and …

It is known that a knot/link can be nullified, ie can be made into the trivial knot/link, by
smoothing some crossings in a projection diagram of the knot/link. The minimum number of …

For ICQ and k\knots in S3, let the band sum of k0 and k\be defined as follows: imbed k0 and
k\into disjoint 3-balls in S3\let b: I x/—> S3 be an imbedding such that b~ ι {ki}= I x {/},/= 0, 1; …

In this paper, we consider the nullification numbers ni (L) of the 249 prime knots up to 10
crossings to an unlink with i components. This extends an existing table of knot nullification …

For a pair of knots $ K_1 $ and $ K_0 $, we consider the set of four-tuples of integers $(g,
c_0, c_1, c_2) $ for which there is a cobordism from $ K_1 $ to $ K_0 $ of genus $ g …