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X-WR-CALDESC:Évènements pour LMNO · Laboratoire de mathématiques Nicolas Oresme
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DTSTART;TZID=Europe/Paris:20230926T140000
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DTSTAMP:20260411T213500
CREATED:20231120T081114Z
LAST-MODIFIED:20231120T081115Z
UID:80-1695736800-1695740400@lmno.unicaen.fr
SUMMARY:Crystallographic structures and braid theory
DESCRIPTION:Exposé dans le cadre du séminaire d’algèbre et de géométrie \n\n\n\nOrateur : Oscar Ocampo (Salvador de Bahia) \n\n\n\nLet M be a compact surface without boundary\, and n≥2. We analyse the quotient group Bn(M)/Γ2(Pn(M)) of the surface braid group Bn(M) by the commutator subgroup Γ2(Pn(M)) of the pure braid group Pn(M). If M is different from the 2-sphere S2\, we prove that Bn(M)/Γ2(Pn(M))≅Pn(M)/Γ2(Pn(M))⋊φSn\, and that Bn(M)/Γ2(Pn(M)) is a crystallographic group if and only if M is orientable.  \n\n\n\nIf M is orientable\, we show a number of results regarding the structure of Bn(M)/Γ2(Pn(M)). Finally\, we construct a family of Bieberbach subgroups G˜n\,g of Bn(M)/Γ2(Pn(M)) of dimension 2ng and whose holonomy group is the finite cyclic group of order n\, and if Xn\,g is a flat manifold whose fundamental group is G˜n\,g\, we prove that it is an orientable Kähler manifold that admits Anosov diffeomorphisms. Joint work with Daciberg Lima Gonçalves\, John Guaschi and Carolina de Miranda e Pereiro.
URL:https://lmno.unicaen.fr/evenement/crystallographic-structures-and-braid-theory/
LOCATION:Caen · Campus 2 · Sciences 3 · Salle S3-247\, UFR des Sciences\, Sciences 3\, 6 Boulevard Maréchal Juin\, Caen\, 14000\, France
CATEGORIES:Algèbre et géométrie
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