Noncommutative Geometry Seminar

Date: September 29, 2017

Time: 2:00PM - 3:00PM

Location: *BLOC 220*

Speaker: Sherry Gong, Massachusetts Institute of Technology

Title: Marked link invariants: Khovanov, instanton, and binary dihedral invariants for marked links

Abstract: 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 (Kronheimer and Mrowka, \textit{Khovanov homology is an unknot-detector}) collapses on the $E_2$ page for alternating links. We moreover show that the Khovanov homology we introduce for alternating links does not depend on $\omega$; thus, the instanton homology also does not depend on $\omega$ for 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 $\omega$. (* Note the special time and room.)