On the slice genus of links

We define Casson–Gordon $σ$ –invariants for links and give a lower bound of the slice genus of a link in terms of these invariants. We study as an example a family of two component links of genus $h$ and show that their slice genus is $h$ , whereas the Murasugi–Tristram inequality does not obstruct this link from bounding an annulus in the 4–ball.

Keywords

Casson–Gordon invariants, link signatures

Mathematical Subject Classification 2000

Primary: 57M25

Secondary: 57M27

References

Forward citations

Publication

Received: 23 October 2002

Revised: 5 July 2003

Accepted: 5 September 2003

Published: 29 September 2003

Authors

Vincent Florens
Laboratoire I.R.M.A. Université Louis Pasteur Strasbourg France

Patrick M Gilmer
Department of Mathematics Louisiana State University Baton Rouge LA 70803 USA

Volume 3, issue 2 (2003)

Vincent Florens and Patrick M Gilmer