The link concordance invariant from Lee homology

We use the knot homology of Khovanov and Lee to construct link concordance invariants generalizing the Rasmussen $s$ –invariant of knots. The relevant invariant for a link is a filtration on a vector space of dimension $2^{| L |}$ . The basic properties of the $s$ –invariant all extend to the case of links; in particular, any orientable cobordism $Σ$ between links induces a map between their corresponding vector spaces which is filtered of degree $χ (Σ)$ . A corollary of this construction is that any component-preserving orientable cobordism from a $Kh$ –thin link to a link split into $k$ components must have genus at least $⌊ k ∕ 2 ⌋$ . In particular, no quasi-alternating link is concordant to a split link.

PDF Access Denied

Warning: We have not been able to recognize your IP address 47.88.87.18 as that of a subscriber to this journal. Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form.

Or, visit our subscription page for instructions on purchasing a subscription. You may also contact us at contact@msp.org or by using our contact form.

Or, you may purchase this single article for USD 29.95:

Keywords

Khovanov homology, link concordance, link cobordism, Rasmussen s-invariant, slice genus

Mathematical Subject Classification 2010

Primary: 57M25, 57M27, 57Q60

References

Publication

Received: 25 July 2011

Revised: 9 February 2012

Accepted: 14 February 2012

Published: 7 May 2012

Authors

John Pardon
Department of Mathematics Stanford University 450 Serra Mall Building 380 Stanford CA 94305 USA
http://math.stanford.edu/~pardon/

Volume 12, issue 2 (2012)

John Pardon

Abstract