A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

KeeTaek Kim; Taketo Sano

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arXiv · 2503.05414

A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

KeeTaek Kim·Taketo Sano

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Abstract

We introduce a diagrammatic approach to Rasmussen's $s$-invariant, based on Bar-Natan's reformulation of Khovanov homology for tangles and cobordisms. This method enables a local computation of $s$ from a tangle decomposition of a knot diagram. As an application, we compute the $s$-invariants of all 3-strand pretzel knots.

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BibTeX RIS

KeeTaek Kim, Taketo Sano. 2025-03-07. A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms. https://arxiv.org/abs/2503.05414

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