Release Time:2019-03-12  Hits:

Indexed by: Journal Article

Date of Publication: 2017-01-01

Journal: BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY

Included Journals: SCIE

Volume: 54

Issue: 1

Page Number: 1-15

ISSN: 1015-8634

Key Words: homologically thin knot; Jones polynomial; signature; Kanenobu knots; Khovanov cohomology; odd Khovanov homology

Abstract: Kanenobu has given infinite families of knots with the same HOMFLY polynomial invariant but distinct Alexander module structure. In this paper, we give a recursive formula for the Khovanov cohomology of all Kanenobu knots K (p, q), where p and q are integers. The result implies that the rank of the Khovanov cohomology of K (p, q) is an invariant of p | (q. Our computation uses only the basic long exact sequence in knot homology and some results on homologically thin knots.