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A note on the local relations in geometric formalism of Khovanov homology theory

Kokoro Tanaka

Department of Mathematics, Tokyo Gakugei University, 4-1-1 Nukuikita-machi, Koganei-shi, Tokyo 184-8501, Japan

E-mail Address: kotanaka@u-gakugei.ac.jp

https://doi.org/10.1142/S0218216516200017Cited by:0 (Source: Crossref)

Abstract

In this short note, we prove that the sphere and 4-tube relations “almost” imply the torus relation in Bar-Natan’s geometric formalism of Khovanov homology theory. As an application, we point out that the invariance and the functoriality can be proved without using the torus relation.

Keywords:

AMSC: 57M25, 18E05

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