Joint topology/noncommutative geometry seminar

Speaker: Sherry Gong (MIT)

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, 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 $\omega$.