The smooth 4-genus of (the rest of) the prime knots through 12 crossings
Mark Brittenham, Susan Hermiller
TL;DR
This paper completes the calculation of the smooth 4-genus for all prime knots with 12 or fewer crossings, filling a significant gap in knot theory data.
Contribution
It provides the first complete determination of the smooth 4-genus for all prime knots with up to 12 crossings.
Findings
Smooth 4-genus values computed for previously unknown knots
Complete dataset for prime knots with ≤12 crossings
Advances understanding of knot complexity and properties
Abstract
We compute the smooth 4-genera of the prime knots with 12 crossings whose values, as reported on the KnotInfo website, were unknown. This completes the calculation of the smooth 4-genus for all prime knots with 12 or fewer crossings.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory