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SUMMARY:Homotopy type of equivariant symplectomorphisms of rational ruled
surfaces
DTSTART;VALUE=DATE-TIME:20220921T060000Z
DTEND;VALUE=DATE-TIME:20220921T070000Z
DTSTAMP;VALUE=DATE-TIME:20230130T011902Z
UID:indico-event-8580@cern.ch
DESCRIPTION:Abstract: In this talk\, we present results on the homotopy ty
pe of the\ngroup of equivariant symplectomorphisms of $S^2 \\times S^2$ an
d\n$\\mathbb{C}P^2$ blown up once under the presence of a Hamiltonian circ
le\nactions. We prove that the group of equivariant symplectomorphisms is\
nhomotopy equivalent to either a torus\, or to the homotopy pushout of two
\ntori depending on whether the circle action extends to a single toric\na
ction or to exactly two nonequivalent toric actions. Our results rely on\n
J-holomorphic techniques\, on Delzant’s classification of toric actions\
,\nand on Karshon’s classification of Hamiltonian circle actions on\n4-m
anifolds. Time permitting we will explain results of a similar flavour\non
the homotopy type of $\\mathbb{Z}_n$ equivariant symplectomorphisms for\n
a large family of finite cyclic groups in the Hamiltonian group. This is\n
based on joint work with Martin Pinsonnault.\n\nhttps://indico.tifr.res.in
/indico/conferenceDisplay.py?confId=8580
LOCATION: AG-77
URL:https://indico.tifr.res.in/indico/conferenceDisplay.py?confId=8580
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