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SUMMARY:The homology of big mapping class groups - Martin Palmer-Anghel (I
 nstitute of Mathematics of the Romanian Academy)
DTSTART:20230612T150000Z
DTEND:20230612T160000Z
UID:TALK199885@talks.cam.ac.uk
DESCRIPTION:Mapping class groups of infinite-type surfaces ("big mapping c
 lass groups") have recently become the subject of intensive study\, inspir
 ed by their connections with dynamical systems and geometric group theory.
  However\, their homology above degree one has so far been very little und
 erstood. I will describe two results\, from joint work with Xiaolei Wu\, t
 hat exhibit contrasting behaviour of the homology of big mapping class gro
 ups. First\, using methods of homological stability\, we find an uncountab
 le family of big mapping class groups (including notably the mapping class
  group of the disc minus a Cantor set) whose integral homology vanishes in
  all positive degrees. Second\, by entirely different methods\, we find an
 other uncountable family of big mapping class groups whose integral homolo
 gy is uncountable in each positive degree.
LOCATION:Seminar Room 1\, Newton Institute
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