# Toric reflection groups

@inproceedings{Gobet2021ToricRG, title={Toric reflection groups}, author={Thomas Gobet}, year={2021} }

Several finite complex reflection groups have a braid group which is isomorphic to a torus knot group. The reflection group is obtained from the torus knot group by declaring meridians to have order k for some k ≥ 2, and meridians are mapped to reflections. We study all possible quotients of torus knot groups obtained by requiring meridians to have finite order. Using the theory of J-groups of Achar and Aubert, we show that these groups behave like (in general infinite) complex reflection…

## One Citation

### A new Garside structure on torus knot groups and some complex braid groups

- Mathematics
- 2022

. Several distinct Garside monoids having torus knot groups as groups of fractions are known. For n, m ≥ 2 two coprime integers, we introduce a new Garside monoid M ( n, m ) having as Garside group…

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