A Rasmussen invariant for links in \mathbbRP³

2023/01/24 by Ciprian Manolescu, Manolescu, Ciprian, Michael Willis +1
Mathematics · Medicine · #57K18 (Primary) 57R85 (Secondary) #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)

paper · pdf · doi:10.48550/arxiv.2301.09764

openalex publication_date 2023/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Asaeda-Przytycki-Sikora, Manturov, and Gabrovšek extended Khovanov homology to links in \mathbbRP³. We construct a Lee-type deformation of their theory, and use it to define an analogue of Rasmussen's s-invariant in this setting. We show that the s-invariant gives constraints on the genera of link cobordisms in the cylinder I × \mathbbRP³. As an application, we give examples of freely 2-periodic knots in S³ that are concordant but not standardly equivariantly concordant.

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