Minimal generating and normally generating sets for the braid and mapping class groups of D-2,S-2 and RP2

Autor(es)

Goncalves, Daciberg Lima ^[1] ; Guaschi, John ^[2]

Afiliação do(s) autor(es)

^[1] IME USP, Dept Matemat, BR-05314970 Sao Paulo - Brazil

^[2] Univ Caen Basse Normandie, CNRS, UMR 6139, Lab Math Nicolas Oresme, F-14032 Caen - France

• Tipo de documento: Artigo Científico
• Fonte: MATHEMATISCHE ZEITSCHRIFT; v. 274, n. 1-2, p. 667-683, JUN 2013.
• Citações Web of Science: 0

Resumo

We consider the (pure) braid groups and , where is the -sphere or the real projective plane . We determine the minimal cardinality of (normal) generating sets of these groups, first when there is no restriction on , and secondly when consists of elements of finite order. This improves on results of Berrick and Matthey in the case of , and extends them in the case of . We begin by recalling the situation for the Artin braid groups (). As applications of our results, we answer the corresponding questions for the associated mapping class groups, and we show that for or , the induced action of on is trivial, being the configuration space of . (AU)

• Processo FAPESP: 08/57607-6 - Topologia algébrica geométrica e diferencial
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Temático
• Processo FAPESP: 09/54745-1 - Estudo dos subgrupos virtualmente cíclicos das tranças do plano projetivo e a cisão das sequências generalizadas tipo Fadell-Neuwirth do plano projetivo
• Beneficiário: Daciberg Lima Gonçalves
• Modalidade de apoio: Auxílio à Pesquisa - Regular