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• W2155771824 abstract "Let M be a compact, connected surface, possibly with a finite set of points removed from its interior. Let d,n be positive integers, and let N be a d-fold covering space of M. We show that the covering map induces an embedding of the n-th braid group B_n(M) of M in the (dn)-th braid group B_{dn}(N) of N, and give several applications of this result. First, we classify the finite subgroups of the n-th braid group of the real projective plane, from which we deduce an alternative proof of the classification of the finite subgroups of the mapping class group of the n-punctured real projective plane due to Bujalance, Cirre and Gamboa. Secondly, using the linearity of B_{n} due to Bigelow and Krammer, we show that the braid groups of compact, connected surfaces of low genus are linear." @default.
• W2155771824 created "2016-06-24" @default.
• W2155771824 creator A5015797376 @default.
• W2155771824 creator A5049208448 @default.
• W2155771824 date "2009-06-15" @default.
• W2155771824 modified "2023-09-25" @default.
• W2155771824 title "Embeddings of the braid groups of covering spaces, classification of the finite subgroups of the braid groups of the real projective plane, and linearity of braid groups of low-genus surfaces" @default.
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• W2155771824 hasPublicationYear "2009" @default.
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