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2009 Functoriality for the $\mathfrak{su}_3$ Khovanov homology
David Clark
Algebr. Geom. Topol. 9(2): 625-690 (2009). DOI: 10.2140/agt.2009.9.625

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.

Citation

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David Clark. "Functoriality for the $\mathfrak{su}_3$ Khovanov homology." Algebr. Geom. Topol. 9 (2) 625 - 690, 2009. https://doi.org/10.2140/agt.2009.9.625

Information

Received: 13 January 2009; Revised: 2 March 2009; Accepted: 5 March 2009; Published: 2009
First available in Project Euclid: 20 December 2017

zbMATH: 1165.57005
MathSciNet: MR2482322
Digital Object Identifier: 10.2140/agt.2009.9.625

Subjects:
Primary: 57M25
Secondary: 57M27, 57Q45

Rights: Copyright © 2009 Mathematical Sciences Publishers

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Vol.9 • No. 2 • 2009
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