Genus generators and the positivity of the signature

Details Genus generators and the positivity of the signature Genus generators and the positivity of the signature

2009-07-06

arxiv.org/abs/0907.1038v1

Algebr. Geom. Topol. 6 (2006) 2351-2393

Mathematics

Geometric Topology

This is the version published by Algebraic & Geometric Topology on 13 December 2006

Scientific paper

10.2140/agt.2006.6.2351

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 greater than or equal to n is dominated by a finite subset of itself in the sense of Taniyama's partial order.

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