Decomposition of the first Vassiliev derivative of Khovanov homology and its application

Autor:	Yoshida, Jun
Rok vydání:	2020
Předmět:	Mathematics - Geometric Topology Mathematics - Quantum Algebra 57K18 (Primary) 57K16 57K10 57K12 (Secondary)
Druh dokumentu:	Working Paper
Popis:	Khovanov homology extends to singular links via a categorified analogue of Vassiliev skein relation. In view of Vassiliev theory, the extended Khovanov homology can be seen as Vassiliev derivatives of Khovanov homology. In this paper, we develop a new method to compute the first derivative. Namely, we introduce a complex, called a crux complex, and prove that the Khovanov homologies of singular links with unique double points are homotopic to cofibers of endomorphisms on crux complexes. Since crux complexes are actually small for some links, the result enables a direct computation of the first derivative of Khovanov homology. Furthermore, it together with a categorified Vassiliev skein relation provides a brand-new method for the computation of Khovanov homology. In fact, we apply the result to determine the Khovanov complexes of all twist knots in a universal way. Comment: 47 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2007.15867 Zobrazit plný text záznamu View this record from Arxiv