Cobordisms to weakly splittable links
Stefan Friedl, Mark Powell
TL;DR
This paper establishes a lower bound on the genus of cobordisms from links with non-zero Alexander polynomial to weakly m-split links, generalizing previous results and contributing to knot theory and link cobordism understanding.
Contribution
It introduces a new genus bound for cobordisms to weakly m-split links, extending Pardon's recent findings in the field.
Findings
Genus of cobordism is at least (m-1)/2 for certain links.
Links with non-zero Alexander polynomial have constrained cobordism genus.
Generalizes previous results by J. Pardon.
Abstract
We show that if a link L with non-zero Alexander polynomial admits a locally flat cobordism to a `weakly m-split link', then the cobordism must have genus at least (m-1)/2. This generalises a recent result of J. Pardon.
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Taxonomy
TopicsGeometric and Algebraic Topology · Homotopy and Cohomology in Algebraic Topology · Advanced Combinatorial Mathematics