Functoriality for the 𝔰𝔲3 Khovanov homology

Clark, David

doi:10.2140/agt.2009.9.625

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Functoriality for the $\mathfrak{su}_3$ Khovanov homology

David Clark

Algebraic & Geometric Topology 9 (2009) 625–690

DOI: 10.2140/agt.2009.9.625

Abstract

We prove that the categorified ${s u}_{3}$ quantum link invariant is functorial with respect to tangle cobordisms. This is in contrast to the categorified ${s u}_{2}$ 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/

Volume 9, issue 2 (2009)