Lower central series, surface braid groups, surjections and permutations
| Autor: | Paolo Bellingeri, Daciberg Lima Gonçalves, John Guaschi |
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| Přispěvatelé: | Laboratoire de Mathématiques Nicolas Oresme (LMNO), Centre National de la Recherche Scientifique (CNRS)-Université de Caen Normandie (UNICAEN), Normandie Université (NU)-Normandie Université (NU), Université de Caen Normandie (UNICAEN), Normandie Université (NU), Centre National de la Recherche Scientifique (CNRS), Instituto de Matemática e Estatística (IME), Universidade de São Paulo (USP) |
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
TEORIA DOS GRUPOS General Mathematics 010102 general mathematics Braid group Boundary (topology) Geometric Topology (math.GT) Group Theory (math.GR) Surface (topology) Central series 01 natural sciences [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR] Surjective function Mathematics - Geometric Topology Symmetric group [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 0103 physical sciences FOS: Mathematics 010307 mathematical physics 0101 mathematics Bijection injection and surjection Mathematics - Group Theory Mathematics |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP Math. Proc. Cambridge Philos. Soc. Math. Proc. Cambridge Philos. Soc., In press |
| ISSN: | 1469-8064 0305-0041 |
| DOI: | 10.1017/s0305004121000244 |
| Popis: | Generalising previous results on classical braid groups by Artin and Lin, we determine the values of m, n ∈ $\mathbb N$ 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. |
| Databáze: | OpenAIRE |
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