Crystallographic groups and flat manifolds from surface braid groups

@article{Gonccalves2021CrystallographicGA,
  title={Crystallographic groups and flat manifolds from surface braid groups},
  author={Daciberg Lima Gonccalves and John Guaschi and Oscar Ocampo and Carolina de Miranda e Pereiro},
  journal={Topology and its Applications},
  year={2021},
  volume={293},
  pages={107560}
}
Abstract Let M be a compact surface without boundary, and n ≥ 2 . We analyse the quotient group B n ( M ) / Γ 2 ( P n ( M ) ) of the surface braid group B n ( M ) by the commutator subgroup Γ 2 ( P n ( M ) ) of the pure braid group P n ( M ) . If M is different from the 2-sphere S 2 , we prove that B n ( M ) / Γ 2 ( P n ( M ) ) ≅ P n ( M ) / Γ 2 ( P n ( M ) ) ⋊ φ S n , and that B n ( M ) / Γ 2 ( P n ( M ) ) is a crystallographic group if and only if M is orientable. If M is orientable, we prove… Expand
Virtual braid groups, virtual twin groups and crystallographic groups
Let n ≥ 2. Let V Bn (resp. V Pn) be the virtual braid group (resp. the pure virtual braid group), and let V Tn (resp. PV Tn) be the virtual twin group (resp. the pure virtual twin group). Let Π beExpand

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