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SUMMARY:CAT(0) cube complex for virtual Artin groups
DTSTART:20261002T120000Z
DTEND:20261002T130000Z
DTSTAMP:20261012T003300Z
UID:indico-event-17413@indico.math.cnrs.fr
DESCRIPTION:Speakers: José Gálvez Mateos (Instituto de Matemáticas de l
 a Universidad de Sevilla (IMUS) and Departamento de Álgebra\, Universidad
  de Sevilla\, Spain.)\n\nVirtual Artin groups\, recently introduced as a n
 atural generalization of virtual braid groups\, unify the structure of Art
 in-Tits groups and Coxeter groups through mixed interaction relations. In 
 this talk\, we construct a geometric object for studying these groups: a c
 ellular complex endowed with a natural cube complex structure $\\Xi_{\\mat
 hcal{D}}$\, associated with any elemental complex $\\mathcal{D}$.   We pr
 ove that $\\Xi_{\\mathcal{D}}$ is connected\, simply connected\, and local
 ly regular. The virtual Artin group acts on $\\Xi_{\\mathcal{D}}$ regularl
 y\, cocompactly\, and by isometries\, with cell stabilizers given precisel
 y by parabolic subgroups. Finally\, we characterize the metric properties 
 of this space\, showing that $\\Xi_{\\mathcal{D}}$ is non-positively curve
 d in the sense of CAT(0) if and only if $\\mathcal{D}$ is a flag complex.\
 n\nhttps://indico.math.cnrs.fr/event/17413/
LOCATION:Salle de séminaire (Orléans institut Denis Poisson)
URL:https://indico.math.cnrs.fr/event/17413/
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