Genera of two-component alternating links
Noboru Ito, Nodoka Kawajiri
TL;DR
This paper extends known results about non-orientable genera from alternating knots to two-component alternating links, showing a unified way to determine genera based on splice sequences and correction terms.
Contribution
It introduces a unified framework for calculating both orientable and non-orientable genera of two-component alternating links using splice sequences.
Findings
Unified formula for genera based on splice sequences
Explicit correction term for genus calculation
Extension of previous results from knots to links
Abstract
We extend the equality-type results of Ito--Takimura and Kindred for the non-orientable genera of alternating knots to the setting of two-component alternating links. We show that, for such links, a unified quantity capturing both orientable and non-orientable genera is completely determined by the splice sequence realizing the splice-unknotting number up to an explicit correction term.
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Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Geometry and complex manifolds