#### Volume 6, issue 5 (2006)

 Recent Issues
 The Journal About the Journal Subscriptions Editorial Board Editorial Interests Editorial Procedure Submission Guidelines Submission Page Author Index To Appear 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 $\ge n$ 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
Primary: 57M25
Secondary: 57N70