Instantons and Khovanov skein homology on $I\times T^{2}$

Yi Xie; Boyu Zhang

doi:10.4171/qt/184

JournalsqtVol. 16, No. 1pp. 75–115

Instantons and Khovanov skein homology on $I \times T^{2}$

Yi Xie
Peking University, Beijing, P. R. China
Boyu Zhang
Princeton University, College Park, USA

$Instantons and Khovanov skein homology on $I\times T^{2}$ cover$

Download PDF

This article is published open access under our Subscribe to Open model.

Abstract

Asaeda, Przytycki, and Sikora (2004) defined a generalization of Khovanov homology for links in $I$ -bundles over compact surfaces. We prove that, for a link $L \subset (- 1, 1) \times T^{2}$ , 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 ${0} \times T^{2}$ . We also prove that Asaeda–Przytycki–Sikora homology detects the unlink and torus links in $(- 1, 1) \times T^{2}$ .

Cite this article

Yi Xie, Boyu Zhang, Instantons and Khovanov skein homology on $I \times T^{2}$ . Quantum Topol. 16 (2025), no. 1, pp. 75–115

DOI 10.4171/QT/184