Lower central series, surface braid groups, surjections and permutations

Paolo Bellingeri (1, 2, 3, 4) , Daciberg Lima Gonçalves (5, 6) , John Guaschi (1, 2, 3, 4)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme
2 UNICAEN - Université de Caen Normandie
3 CNRS - Centre National de la Recherche Scientifique
4 NU - Normandie Université
5 IME - Instituto de Matemática e Estatística
6 USP - Universidade de São Paulo = University of São Paulo

Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n ∈ N for which there exists a surjection between the n-and m-string braid groups of an orientable surface without boundary. This result is essentially based on specific properties of their lower central series, and the proof is completely combinatorial. We provide similar but partial results in the case of orientable surfaces with boundary components and of non-orientable surfaces without boundary. We give also several results about the classification of different representations of surface braid groups in symmetric groups.

Domaines: Topologie géométrique [math.GT]; Théorie des groupes [math.GR]

Paolo Bellingeri, Daciberg Lima Gonçalves, John Guaschi. Lower central series, surface braid groups, surjections and permutations. Mathematical Proceedings of the Cambridge Philosophical Society, 2022, 172 (2), pp.373-399. ⟨10.1017/S0305004121000244⟩. ⟨hal-01906514⟩