Quantum Topology


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Volume 5, Issue 1, 2014, pp. 1–59
DOI: 10.4171/QT/46

Published online: 2014-03-03

A categorification of quantum $\mathfrak{sl}_3$ projectors and the $\mathfrak{sl}_3$ Reshetikhin–Turaev invariant of tangles

David E. V. Rose[1]

(1) Duke University, USA

We construct a categorification of the quantum $\mathfrak{sl}_3$ projectors, the $\mathfrak{sl}_3$ analog of the Jones–Wenzl projectors, as the stable limit of the complexes assigned to $k$-twist torus braids (as $k \to \infty$) in a suitably shifted version of Morrison and Nieh’s geometric formulation of $\mathfrak{sl}_3$ link homology [14] We use these projectors to give a categorification of the $\mathfrak{sl}_3$ Reshetikhin–Turaev invariant of framed tangles.

Keywords: Categorification, Jones–Wenzl projectors, $\mathfrak{sl}_3$ spider, Khovanov homology, quantum groups

Rose David: A categorification of quantum $\mathfrak{sl}_3$ projectors and the $\mathfrak{sl}_3$ Reshetikhin–Turaev invariant of tangles. Quantum Topol. 5 (2014), 1-59. doi: 10.4171/QT/46