Khovanov homology and binary dihedral representations for marked links

Sherry Gong

doi:10.1016/j.geomphys.2018.10.014

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arXiv · 1801.02585

Khovanov homology and binary dihedral representations for marked links

Sherry Gong

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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 introduced in \cite{KM_unknot} 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 $\omega$.

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BibTeX RIS

Sherry Gong. 2018-01-08. Khovanov homology and binary dihedral representations for marked links. https://doi.org/10.1016/j.geomphys.2018.10.014

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