Khovanov homology and binary dihedral representations for marked links

[摘要] We introduce a version of Khovanov homology for alternating links with marking data, omega, inspired by instanton theory. We show that the analogue of the spectral sequence from Khovanov homology to singular instanton homology introduced in Kronheimer and Mrowka (2011) for this marked Khovanov homology collapses on the E-2 page for alternating links. We moreover show that for non-split links the Khovanov homology we introduce for alternating links does not depend on omega; thus, the instanton homology also does not depend on omega for non-split alternating links. Finally, we study a version of binary dihedral representations for links with markings, and show that for links of non-zero determinant, this also does not depend on omega. (C) 2019 Elsevier B.V. All rights reserved.

[发布日期] 2019-06-01

[效力级别]  Proceedings Paper

[关键词] Knot theory;Low dimensional topology;Gauge theory