Khomotopy type via simplicial complexes and presimplicial sets

Marithania Silvero (Universidad de Sevilla)

At the end of the past century, Mikhail Khovanov introduced the first homological invariant, now known as Khovanov homology, as a categorification of Jones polynomial. It is a bigraded homology supported in homological and quantum gradings. Given a link diagram, we refer to the maximal (resp. second-to-maximal) quantum grading such that the associated Khovanov complex is non-trivial as extreme (resp. almost extreme) grading.

In this talk we present a new approach to the geometrization of Khovanov homology in terms of simplicial complexes and presimplicial sets, for the extreme and almost-extreme gradings, respectively. We also study the relations of these models with Khovanov spectra, introducec by Robert Lipshitz and Sucharit Sarkar as a spatial refinement of Khovanov homology.

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