Instantons and Khovanov skein homology on I× T²

2020/05/26 by Yi Xie, Xie, Yi, Boyu Zhang +1
Mathematics · Medicine · #57M27 #57R58 #Botulinum Toxin and Related Neurological Disorders #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2005.12863

openalex publication_date 2020/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Asaeda, Przytycki and Sikora defined a generalization of Khovanov homology for links in I-bundles over compact surfaces. We prove that for a link L⊂ (-1,1)× T², the Asaeda-Przytycki-Sikora homology of L has rank 2 with ℤ/2-coefficients if and only if L is isotopic to an embedded knot in \0\× T².

Related

• Instanton homology and knot detection on thickened surfaces
• Khovanov homology for links in #^r(S²× S¹)
• Earrings, sutures and pointed links
• Instantons, Bar-Natan homology, and some concordance invariants of knots
• Twisted skein homology