Secondary Braid Groups

2020/01/24 by Sebastian Baader, Baader, Sebastian, Michael Lönne +1 · 1 citation
Computer Science · Mathematics · #20F36 (Secondary) #32S55 #57M05 (Primary) 57M27 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings, Modules, and Algebras #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.2001.09098

openalex publication_date 2020/01/24 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We generalize presentations of the fundamental group of discriminant complements and arrive at a class of presentations associated naturally with words in the free monoid of the alphabet σ₁,…,σ_n-1. Our study addresses invariance properties of these presentations and the presented groups under various operations on the words. In particular we prove that the group does only depend on the corresponding element in the positive braid monoid, and under mild hypotheses only on its conjugacy class in the braid group.

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