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Split link detection for sl(P) link homology in characteristic P

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arxiv 2112.09110 v2 pith:TM7ZT5SA submitted 2021-12-16 math.GT

Joshua Wang This is my paper · ORCID
classification math.GT
keywords homologylinkcoefficientssplitdetectionmathbfargumentcharacteristic
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abstract

If $P$ is a prime number, we show that reduced $\mathfrak{sl}(P)$ link homology with coefficients in $\mathbf{Z}/P$ detects split links. The argument uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. When $P = 2$, we recover Lipshitz-Sarkar's split link detection result for Khovanov homology with $\mathbf{Z}/2$ coefficients.

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  1. Remarks on some infinitesimal symmetries of Khovanov--Rozansky homologies in finite characteristic

    math.GT 2024-12 conditional novelty 6.0 of 10

    A p-differential algebra argument reproves base point independence for characteristic-p Khovanov-Rozansky homology and yields new sl2-symmetry consequences for link homology.

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