Genus generators and the positivity of the signature

Stoimenow, Alexander¹

¹Research Institute for Mathematical Sciences, Kyoto University, Kyoto 606-8502, Japan

Algebraic and Geometric Topology, Tome 6 (2006) no. 5, pp. 2351-2393

Résumé

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.

Détail

DOI : 10.2140/agt.2006.6.2351

Keywords: signature, genus, positive knot, Taniyama's partial order

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