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2004 An invariant of link cobordisms from Khovanov homology
Magnus Jacobsson
Algebr. Geom. Topol. 4(2): 1211-1251 (2004). DOI: 10.2140/agt.2004.4.1211


In [Duke Math. J. 101 (1999) 359–426], Mikhail Khovanov constructed a homology theory for oriented links, whose graded Euler characteristic is the Jones polynomial. He also explained how every link cobordism between two links induces a homomorphism between their homology groups, and he conjectured the invariance (up to sign) of this homomorphism under ambient isotopy of the link cobordism. In this paper we prove this conjecture, after having made a necessary improvement on its statement. We also introduce polynomial Lefschetz numbers of cobordisms from a link to itself such that the Lefschetz polynomial of the trivial cobordism is the Jones polynomial. These polynomials can be computed on the chain level.


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Magnus Jacobsson. "An invariant of link cobordisms from Khovanov homology." Algebr. Geom. Topol. 4 (2) 1211 - 1251, 2004.


Received: 24 January 2004; Revised: 18 November 2004; Accepted: 8 December 2004; Published: 2004
First available in Project Euclid: 21 December 2017

zbMATH: 1072.57018
MathSciNet: MR2113903
Digital Object Identifier: 10.2140/agt.2004.4.1211

Primary: 57Q45
Secondary: 57M25

Rights: Copyright © 2004 Mathematical Sciences Publishers


Vol.4 • No. 2 • 2004
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