Algebraic & Geometric Topology

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

David Clark

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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.

Article information

Algebr. Geom. Topol., Volume 9, Number 2 (2009), 625-690.

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

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 57M27: Invariants of knots and 3-manifolds 57Q45: Knots and links (in high dimensions) {For the low-dimensional case, see 57M25}

Khovanov categorification link cobordism su(3) quantum invariant


Clark, David. Functoriality for the $\mathfrak{su}_3$ Khovanov homology. Algebr. Geom. Topol. 9 (2009), no. 2, 625--690. doi:10.2140/agt.2009.9.625.

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