Quid of Braid Groups and Homological Representations

par Thiago Brevidelli (IMT, Université de Toulouse)

mercredi 30 sept. 2026, 18:00 → 19:30 Europe/Paris

Salle Pellos (1R2-207)

Given a group G, it is natural to ask whether or not it is linear, i.e., if G is isomorphic to a subgroup of GL_N(R) for some N and some ring R. In this seminar, we will answer this question for the group G = B_n, the braid group in n strands.

Starting from first principles, we will review the main ideas behind Bigelow's proof of the linearity of B_n. Doing so should take us through a pleasant walk in the realms of mapping class groups and covering theory. We will use these ingredients to construct the so-called homological representations of B_n: a way of representing braids with matrices. If time allows, we may also comment on some related open questions.