A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-07
Primary Topic
Geometric and Algebraic Topology
Type
article
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article

A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

ArXiv.org
Geometric and Algebraic Topology
article

A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms

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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.

ArXiv.org
Openalex Percentile: Top 44%
Geometric and Algebraic Topology
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A diagrammatic approach to the Rasmussen invariant via tangles and cobordisms · ArXiv.org (2025) | TGRS Research Map | TGRS