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SUMMARY:Ends of groups and related invariants - Pénélope Azuelos\, Unive
 rsity of Bristol
DTSTART:20240216T160000Z
DTEND:20240216T170000Z
UID:TALK209293@talks.cam.ac.uk
CONTACT:Alexis Marchand
DESCRIPTION:The number of ends of a group G is an invariant\, introduced b
 y Hopf in the 1940s\, which encodes the number of ways one can "go to infi
 nity" within G. This notion was later generalised in different ways\, by H
 oughton and by Kropholler and Roller\, to study pairs of groups. In this c
 ase\, one is interested in the geometry of a subgroup embedding and\, alth
 ough the situation becomes more complicated\, the number of ends can revea
 l interesting properties of both the ambient group and the subgroup in que
 stion. I will discuss these invariants and various classical results about
  the structure of groups (or subgroup embeddings) with certain numbers of 
 ends. Time permitting\, I will talk about some recent work about group pai
 rs which have two ends in a particularly strong way.
LOCATION:MR13
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