arXiv subjects

Keita Nakagane

Publications and source records attributed to Keita Nakagane.

5 recordsLinked to original sources

arXiv2025

Remark on twists of Frobenius algebra and link homology

We discuss twists on Frobenius algebras in the context of link homology. In his paper in 2006, Khovanov asserted that a twist of a Frobenius algebra yields an isomorphic chain complex on each link diagram. Although the result has been widely accepted for nearly two decades, a subtle gap in the original proof was found in the induction step of the construction of the isomorphism. Following discussion with Khovanov, we decided to provide a new proof. Our proof is based on a detailed analysis of configurations of circles in each state.

math.QA↗

arXiv2024

Computations of HOMFLY homology

Khovanov--Rozansky's HOMFLY homology is determined for all prime knots with up to 11 crossings by direct computations.

math.GT↗

arXiv2020

A full-twisting formula for the HOMFLY polynomial

We introduce a certain class of link diagrams, which includes all closed braid diagrams. We show a generalized version of Kálmán's full-twist formula for the HOMFLY polynomial in the class.

math.GT↗

arXiv2020

Serre duality for Khovanov-Rozansky homology

We prove that the full twist is a Serre functor in the homotopy category of type A Soergel bimodules. As a consequence, we relate the top and bottom Hochschild degrees in Khovanov-Rozansky homology, categorifying a theorem of Kálmán.

math.RT↗

arXiv2018

The action of full twist on the superpolynomial for torus knots

We show, using Mellit's recent results, that Kálmán's full twist formula for the HOMFLY polynomial can be generalized to a formula for superpolynomials in the case of positive toric braids.

math.GT↗