Doubly slice knots and the Casson-Gordon invariants-Reference-Cited by-同舟云学术

Doubly slice knots and the Casson-Gordon invariants

Published:1983 Issue:2 Volume:279 Page:569-588
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Ruberman Daniel

Abstract

We find knots in all dimensions which are algebraically but not geometrically doubly slice. Our new obstructions involve the Casson-Gordon invariants of the finite cyclic covers in odd dimensions and of the infinite cyclic cover in even dimensions. These same invariants provide new criteria for amphicheirality and invertibility of even-dimensional knots.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1983-279-02/S0002-9947-1983-0709569-5/S0002-9947-1983-0709569-5.pdf

Reference29 articles.

1. Branched covers of surfaces in 4-manifolds;Akbulut, Selman;Math. Ann.,1979

2. The index of elliptic operators. III;Atiyah, M. F.;Ann. of Math. (2),1968

3. Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 65;Browder, William,1972

4. A. Casson and C. Gordon, Cobordism of classical knots, preprint, Orsay, 1975.

5. On slice knots in dimension three;Casson, A. J.,1978

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