2025/09/02 by Daciberg Lima Gonçalves, Gonçalves, Daciberg Lima, John Guaschi +3
Computer Science · Mathematics · #Algebraic Topology (math.AT) #Approximation Theory and Sequence Spaces #Coding theory and cryptography #FOS: Mathematics #Geometric Topology (math.GT) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2509.02707
openalex publication_date 2025/09/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study some generalisations to mixed braid groups of the Fadell-Neuwirth short exact sequence and the possible splitting of this sequence. In certain cases, we determine conditions under which the projection from the mixed braid group B_n1,…,nk(M) to B_n1,…, nk-q(M) admits a section, where M is either the torus or the Klein bottle, n1, …, nk,q ∈ ℕ, and 1≤ q ≤ k-1. For k≥ 2 and q=k-1, we show that this projection admits a section if and only if n1 divides ni for all i=2,…, k. We present some partial conclusions in the case k≥ 3 and q=1. To obtain our results, we compute and make use of suitable mixed braid groups of M, as well as certain key quotients that play a central rôle in our analysis.