The average genus of oriented rational links with a given crossing number
Dawn Ray, Yuanan Diao
TL;DR
This paper derives a precise formula for the average minimal genus of oriented rational knots and links based on their crossing number, advancing understanding of their topological complexity.
Contribution
It provides a new exact formula for the average genus of oriented rational knots and links for any crossing number, based on enumeration methods.
Findings
Exact formula for average minimal genus derived
Enumeration of oriented rational knots and links achieved
Results applicable to all crossing numbers
Abstract
In this paper, we enumerate the number of oriented rational knots and the number of oriented rational links with any given crossing number and minimum genus. This allows us to obtain a precise formula for the average minimal genus of oriented rational knots and links with any given crossing number.
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Taxonomy
TopicsGeometric and Algebraic Topology · Topological and Geometric Data Analysis · Homotopy and Cohomology in Algebraic Topology