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Indexed by:期刊论文

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 No.: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.