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SUMMARY:Claudio Llosa Isenrich (KIT)
DTSTART:20221013T130500Z
DTEND:20221013T140000Z
DTSTAMP:20260423T003244Z
UID:GaTO/68
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/GaTO/68/">Fi
 niteness properties\, subgroups of hyperbolic groups\, and complex hyperbo
 lic lattices</a>\nby Claudio Llosa Isenrich (KIT) as part of Geometry and 
 topology online\n\nLecture held in Room B3.02 in the Zeeman Building\, Uni
 versity of Warwick.\n\nAbstract\nHyperbolic groups form an important class
  of finitely generated groups that has attracted much attention in geometr
 ic group theory. We call a group of finiteness type \\(F_n\\) if it has a 
 classifying space with finitely many cells of dimension at most \\(n\\).  
 This generalises finite presentability\, which is equivalent to type \\(F_
 2\\). Hyperbolic groups are of type \\(F_n\\) for all \\(n\\).  It is natu
 ral to ask if subgroups of hyperbolic groups inherit these strong finitene
 ss properties.  We use methods from complex geometry to show that every un
 iform arithmetic lattice with positive first Betti number in \\(\\mathrm{P
 U}(n\, 1)\\) admits a finite index subgroup\, which maps onto the integers
  with kernel of type \\(F_{n−1}\\) but not \\(F_n\\). This answers an ol
 d question of Brady and produces many finitely presented non-hyperbolic su
 bgroups of hyperbolic groups. This is joint work with Pierre Py.\n
LOCATION:https://researchseminars.org/talk/GaTO/68/
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