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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Genus generators and the positivity of the signature

Alexander Stoimenow

Algebraic & Geometric Topology 6 (2006) 2351–2393

arXiv: 0907.1038

Abstract

It is a conjecture that the signature of a positive link is bounded below by an increasing function of its negated Euler characteristic. In relation to this conjecture, we apply the generator description for canonical genus to show that the boundedness of the genera of positive knots with given signature can be algorithmically partially decided. We relate this to the result that the set of knots of canonical genus n is dominated by a finite subset of itself in the sense of Taniyama’s partial order.

Keywords
signature, genus, positive knot, Taniyama's partial order
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57N70
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Publication
Received: 24 June 2006
Accepted: 24 October 2006
Published: 13 December 2006
Authors
Alexander Stoimenow
Research Institute for Mathematical Sciences
Kyoto University
Kyoto 606-8502
Japan
http://www.kurims.kyoto-u.ac.jp/~stoimeno/