$L$-Space Knots in $\mathfrak{sl}_{n}$-like Knot Floer Homology

Tristan Wells

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arXiv · 2610.38927

$L$-Space Knots in $\mathfrak{sl}_{n}$-like Knot Floer Homology

Tristan Wells

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Abstract

It has been of particular interest in recent years to relate categorifications of quantum knot invariants like the Jones polynomial to Floer-theoretic invariants like knot Floer homology using spectral sequences. In pursuit of Rasmussen's conjecture, Dowlin constructed a family of invariants with properties like those of Khovanov and Rozansky's $\mathfrak{sl}_n$-homology theories. In this paper, we explore these invariants for $L$-space knots and thin knots. In particular, for $n\geq 2$ the invariants of thin knots can be computed from a change of coefficients from the minus flavor of knot Floer homology, and the same holds for an $L$-space knot exactly when an explicit condition relating $n$ to its Alexander polynomial is satisfied.

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BibTeX RIS

Tristan Wells. 2026-10-28. $L$-Space Knots in $\mathfrak{sl}_{n}$-like Knot Floer Homology. https://arxiv.org/abs/2610.38927

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