Instantons and Khovanov homology in ${\mathbb{RP}}^3$

Abstract

We study the instanton Floer homology for links in ${\mathbb{RP}}^3$ and compute the second page of Kronheimer--Mrowka's spectral sequence. As an application, we show that Khovanov homology detects the unknot and the projective unknot in ${\mathbb{RP}}^3$.

arXiv comment19 pages, 3 figures; published version

References in corpus (11)

• Categorification of the Kauffman bracket skein module of I-bundles over surfaces
• Knot homology groups from instantons
• Gauge theory and Rasmussen's invariant
• Instantons and odd Khovanov homology
• Instanton Floer homology, sutures, and Heegaard diagrams
• Khovanov homology detects the figure-eight knot
• Khovanov homology detects the Hopf links
• An enhanced Euler characteristic of sutured instanton homology
• Instanton Floer homology, sutures, and Euler characteristics
• Small Dehn surgery and SU(2)
• Khovanov homology detects split links