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SUMMARY:Virtual retractions in graphs of groups and applications - Ashot M
 inasyan (University of Southampton)
DTSTART:20250903T104500Z
DTEND:20250903T114500Z
UID:TALK235543@talks.cam.ac.uk
DESCRIPTION:\n\n\n\nA subgroup H of a group G is a virtual retract if H is
  a retract of a finite index subgroup K in G\, that is\, H<K and there is 
 a homomorphism from K to H whose restriction to H is the identity map. Vir
 tual retracts play an important role in Group Theory\, as they are &ldquo\
 ;nicely&rdquo\; embedded in the ambient group and inherit many properties.
 \n\n\n\nA group has property (VRC) if every cyclic subgroup is a virtual r
 etract. Examples of groups satisfying this property include virtually spec
 ial groups (in the sense of Haglund and Wise)\, and\, more generally\, RFR
 S groups (in the sense of Agol).\n\n\n\n&nbsp\;\n\n\n\nIn the talk I will 
 discuss necessary and sufficient criteria for G to have (VRC)\, where G is
  the fundamental group of a finite graph of groups. In the case when the v
 ertex groups are virtually abelian these criteria can be checked using ele
 mentary tools from Linear Algebra and Euclidean Geometry. I will also disc
 uss applications of (VRC) to algebraic and geometric properties of G.\n\n\
 n\n&nbsp\;\n\n\n\nThe talk will be based on recent joint work with Jon Mer
 ladet\n\n\n\n&nbsp\;\n&nbsp\;\n\n\n\n
LOCATION:Seminar Room 1\, Newton Institute
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