Almost-extreme Khovanov spectra

Morán, Federico Cantero; Silvero, Marithania

doi:10.1007/s00029-021-00706-6

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Concluding Remarks and Future Directions1

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2024

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Cited by 3 publications

(2 citation statements)

References 12 publications

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“…The small steps we plan to address in the future is to work on almost extreme grades of Khovanov homology; compare to [CS2,PS2]. The case of positive 5-braids and extreme Khovanov homology seems to be possible to approach today.…”

Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

Geometric realization of the almost-extreme Khovanov homology of semiadequate links

Przytycki

Silvero

2019

Geom Dedicata

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We introduce the notion of partial presimplicial set and construct its geometric realization. We show that any semiadequate diagram yields a partial presimplicial set leading to a geometric realization of the almost-extreme Khovanov homology of the diagram. We give a concrete formula for the homotopy type of this geometric realization, involving wedge of spheres and a suspension of the projective plane.

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Section: Concluding Remarks and Future Directionsmentioning

confidence: 99%

Geometric realization of the almost-extreme Khovanov homology of semiadequate links

Przytycki

Silvero

2019

Geom Dedicata

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“…González-Meneses, Manchón, and Silvero [GMMS18] gave a geometric description of the extremal Khovanov homology in terms of the all-A and all-B states. Przytycki and Silvero [PS18a,PS18b] and Morán and Silvero [MS18] further study extremal or near extremal Khovanov groups from various different perspectives.…”

mentioning

confidence: 99%

Extremal Khovanov homology of Turaev genus one links

Dasbach

Lowrance

2020

Fund. Math.

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The Turaev genus of a link can be thought of as a way of measuring how non-alternating a link is. A link is Turaev genus zero if and only if it is alternating, and in this viewpoint, links with large Turaev genus are very non-alternating. In this paper, we study Turaev genus one links, a class of links which includes almost alternating links. We prove that the Khovanov homology of a Turaev genus one link is isomorphic to Z in at least one of its extremal quantum gradings. As an application, we compute or nearly compute the maximal Thurston Bennequin number of a Turaev genus one link.

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