Quantum Topology

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Volume 8, Issue 3, 2017, pp. 413–457
DOI: 10.4171/QT/94

Published online: 2017-08-22

Diagrammatics for Coxeter groups and their braid groups

Ben Elias[1] and Geordie Williamson[2]

(1) University of Oregon, Eugene, USA
(2) University of Sydney, Australia

We give a monoidal presentation of Coxeter and braid 2-groups, in terms of decorated planar graphs. This presentation extends the Coxeter presentation. We deduce a simple criterion for a Coxeter group or braid group to act on a category.

Keywords: Coxeter group, braid group, strict group action, Salvetti complex, $K (\pi, 1)$ conjecture, Igusa pictures, diagrammatics

Elias Ben, Williamson Geordie: Diagrammatics for Coxeter groups and their braid groups. Quantum Topol. 8 (2017), 413-457. doi: 10.4171/QT/94