We investigate the Khovanov-Rozansky invariant of a certain tangle and its compositions. Surprisingly the complexes we encounter reduce to ones that are very simple. Furthermore, we discuss a "local" algorithm for computing Khovanov-Rozansky homology and compare our results with those for the "foam" version of sl₃-homology.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-7, author = {Daniel Krasner}, title = {A computation in Khovanov-Rozansky homology}, journal = {Fundamenta Mathematicae}, volume = {205}, year = {2009}, pages = {75-95}, zbl = {1170.57007}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-7} }
Daniel Krasner. A computation in Khovanov-Rozansky homology. Fundamenta Mathematicae, Tome 205 (2009) pp. 75-95. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm203-1-7/