Some link homologies in $ \mathbb{RP}^3 $

William Rushworth

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arXiv · 2603.10832

Some link homologies in $ \mathbb{RP}^3 $

William Rushworth

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Abstract

We introduce extensions of Khovanov homology and the Lee and Bar-Natan spectral sequences for links in $ \mathbb{RP}^3 $. These extensions are distinct to those previously defined by Asaeda-Przytycki-Sikora (and Gabrov\v{s}ek's generalization), Chen, and Manolescu-Willis. The new Lee and Bar-Natan theories each yield Rasmussen invariants (that are distinct to one another). The invariant extracted from the new Lee homology is distinct to that defined by Manolescu-Willis; it is unclear if the same is true for the new Bar-Natan homology and that defined by Chen.

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William Rushworth. 2026-03-11. Some link homologies in $ \mathbb{RP}^3 $. https://arxiv.org/abs/2603.10832

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