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CATEGORIES:Isaac Newton Institute Seminar Series
SUMMARY:The homology of big mapping class groups - Martin
Palmer-Anghel (Institute of Mathematics of the Rom
anian Academy)
DTSTART;TZID=Europe/London:20230612T160000
DTEND;TZID=Europe/London:20230612T170000
UID:TALK199885AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/199885
DESCRIPTION:Mapping class groups of infinite-type surfaces ("b
ig mapping class groups") have recently become the
subject of intensive study\, inspired by their co
nnections with dynamical systems and geometric gro
up theory. However\, their homology above degree o
ne has so far been very little understood. I will
describe two results\, from joint work with Xiaole
i Wu\, that exhibit contrasting behaviour of the h
omology of big mapping class groups. First\, using
methods of homological stability\, we find an unc
ountable family of big mapping class groups (inclu
ding notably the mapping class group of the disc m
inus a Cantor set) whose integral homology vanishe
s in all positive degrees. Second\, by entirely di
fferent methods\, we find another uncountable fami
ly of big mapping class groups whose integral homo
logy is uncountable in each positive degree.
LOCATION:Seminar Room 1\, Newton Institute
CONTACT:
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