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

作者：Goncalves Daciberg Lima; Guaschi John^*

来源：Mathematische Zeitschrift, 2013, 274(1-2): 667-683.

DOI：10.1007/s00209-012-1090-0

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 .

• 出版日期2013-6