An endomorphism of the Khovanov invariant

Abstract

We construct an endomorphism of the Khovanov invariant to prove H-thinness and pairing phenomena of the invariants for alternating links. As a consequence, it follows that the Khovanov invariant of an oriented nonsplit alternating link is determined by its Jones polynomial, signature, and the linking numbers of its components.

To appear in Adv. Math.; Brief summary of Khovanov invariant (math.QA/9908171) and previous result of the author (math.GT/0201105) added

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