Boundary links which are not homotopically split

Kazuaki Kobayashi

KNOTS in WASHINGTON 10 Japan-USA; workshop in Knot Theory
January 23-30, 2000
George Washington University
Washington, DC, USA

Organizers
Kazuaki Kobayashi, Jozef H. Przytycki, Yongwu Rong, Kouki Taniyama, Tatsuya Tsukamoto, Akira Yasuhara

Conference Homepage

Boundary links which are not homotopically split
by
Kazuaki Kobayashi
Tokyo Woman's Christian University

We consider links in the 3-sphere and consider them from the splitness property side. The geometrically split has the strongest splitness property but it is a "product" of knots. In this talk consider the following three kinds of links ,
        1. homotopically split links (h-split links).
        2. boundary links (\partial-links).
        3. link-homotopically trivial in the strong sense (strong h-trivial).
Spetially h-split links is a new class from the splitness property side. An h-split link is a \partial-link and also a strong h-trivial link by definition. So if a given link is a \partial- link but not a strong h-trivial, then it is not h-split. Similarly if a given link is a strong h-trivial link but not a \partial-link, then it is not h-split. In the first part of this talk we shall give such examples. Next we will give an example of a non h-split link which is strong h-trivial and \parial-link. There is no numerical invariant for such links distingushing from h- split links. So we will give some characteristic properties for h-split links and give an example. There is another sequence of links with respest to splitness property side as followings.
        4. split ribbbon links.
        5. ribbon links.
        6. null-cobordant links.
By definitions if L is a split ribbon link, L is a ribbon link and if L is a ribbon link, it is null-cobordant. And if L is a split ribbon link, it is h-split. There are examples of h-split links which are not null-cobordant by calculating the signature of links.

Date received: February 7, 2000