Volume 9, issue 2 (2009)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
Functoriality for the $\mathfrak{su}_3$ Khovanov homology

David Clark

Algebraic & Geometric Topology 9 (2009) 625–690
Abstract

We prove that the categorified su3 quantum link invariant is functorial with respect to tangle cobordisms. This is in contrast to the categorified su2 theory, which was not functorial as originally defined.

We use methods of Morrison and Nieh and Bar-Natan to construct explicit chain maps for each variation of the third Reidemeister move. Then, to show functoriality, we modify arguments used by Clark, Morrison and Walker to show that induced chain maps are invariant, up to homotopy, under Carter and Saito’s movie moves.

Keywords
Khovanov, categorification, link cobordism, su(3), quantum invariant
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27, 57Q45
References
Publication
Received: 13 January 2009
Revised: 2 March 2009
Accepted: 5 March 2009
Published: 9 April 2009
Authors
David Clark
Randolph-Macon College
204 Henry Street
Ashland, VA 23005
USA
http://faculty.rmc.edu/davidclark/