Genus generators and the positivity of the signature

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 $\ge n$ is dominated by a finite subset of itself in the sense of Taniyama’s partial order.