Algebraic & Geometric Topology

Genus generators and the positivity of the signature

Alexander Stoimenow

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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

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

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

signature genus positive knot Taniyama's partial order


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.

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