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SUMMARY:Vanishing results in the homology of big mapping class groups and 
 Thompson-like groups - Martin Palmer\, Leeds
DTSTART:20250221T134500Z
DTEND:20250221T144500Z
UID:TALK224416@talks.cam.ac.uk
CONTACT:Macarena Arenas
DESCRIPTION:Mapping class groups of infinite-type surfaces (a.k.a. "big ma
 pping class groups") have recently become the subject of intensive study. 
 They come in a wild variety of forms and relatively little is currently kn
 own about their homology. I will talk about how homological stability tech
 niques can be used to prove two different vanishing results for their homo
 logy. One is acyclicity (e.g. for the MCG of a disc minus a Cantor set) an
 d the other is the non-existence of non-trivial homology classes supported
  on compact subsurfaces (e.g. for the MCG of the "Loch Ness monster surfac
 e"\, although its homology is uncountably generated). I will also describe
  work in progress using similar techniques to study the homology of certai
 n "Thompson-like" groups\, extending previous work of Szymik and Wahl. Thi
 s represents joint work with Xiaolei Wu.
LOCATION:MR13
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