Braid groups belong to a broad class of groups known as Artin groups, which are defined by presentations of a particular form and have played a major role in geometric group theory and low-dimensional topology in recent years. These groups fall into two classes, finite-type and infinte-type Artin groups. The former come equipped with a powerful combinatorial structure, known as a Garside structure, while the latter are much less understood and present many challenges.
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