Functoriality for the su(3) Khovanov homology

Details Functoriality for the su(3) Khovanov homology Functoriality for the su(3) Khovanov homology

2008-06-03

arxiv.org/abs/0806.0601v1

Mathematics

Geometric Topology

65 pages

Scientific paper

We prove that Morrison and Nieh's categorification of the su(3) quantum knot invariant is functorial with respect to tangle cobordisms. This is in contrast to the categorified su(2) theory, which was not functorial as originally defined. We use methods of 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 under Carter and Saito's movie moves.

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