Lower central series of partitioned braids on surfaces

Jacques Darné (UCLouvain)

Monday 21st February 16:00-17:00 Online

Abstract

Partitioned braid groups (sometimes called "mixed braid groups") are subgroups of the braid group standing between the pure braid group $P_n$ and the whole braid group $B_n$. On the one hand, the lower central series of $B_n$ is almost trivial. On the other hand, the lower central series of $P_n$ is a very rich object, encoding finite type invariants of braids. As a consequence, one can expect partitioned braid groups to display a range of intermediate behaviors, and this is indeed what we observe. In this talk, we will explore these different behaviours and give an answer to the first question one can ask about these lower central series : when do they stop ? Even this simple question turns out to be a difficult one, especially when one considers its generalization to braids on surfaces. However, we will be able to answer it almost completely, leaving open only some cases of partitioned braids on the projective plane.

The talk will be preceded by a tea time at 3:45pm. The Zoom link for the seminar is https://uofglasgow.zoom.us/j/98078798957 and the passcode is the genus of the two-dimensional sphere (4 letters, all lowercase).

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