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.