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On the slice genus of links

Vincent Florens and Patrick M Gilmer

Algebraic & Geometric Topology 3 (2003) 905–920

arXiv: math.GT/0311136

Abstract

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
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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