Algebraic & Geometric Topology

Genus generators and the positivity of the signature

Alexander Stoimenow

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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.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 5 (2006), 2351-2393.

Dates
Received: 24 June 2006
Accepted: 24 October 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796640

Digital Object Identifier
doi:10.2140/agt.2006.6.2351

Mathematical Reviews number (MathSciNet)
MR2286029

Zentralblatt MATH identifier
1128.57008

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57N70: Cobordism and concordance

Keywords
signature genus positive knot Taniyama's partial order

Citation

Stoimenow, Alexander. Genus generators and the positivity of the signature. Algebr. Geom. Topol. 6 (2006), no. 5, 2351--2393. doi:10.2140/agt.2006.6.2351. https://projecteuclid.org/euclid.agt/1513796640


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