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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:The topology of the Gelfand–Zeitlin fiber - Jeff C
arlson\, Imperial
DTSTART;TZID=Europe/London:20211103T160000
DTEND;TZID=Europe/London:20211103T170000
UID:TALK162577AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/162577
DESCRIPTION:Gelfand–Zeitlin systems are a well-known family of
examples in symplectic geometry\, singular Lagran
gian torus fibrations whose total spaces are coadj
oint orbits of an action of a unitary or special o
rthogonal group and whose base spaces are certain
convex polytopes. They are easily defined in terms
of matrices and their truncations\, but do not fi
t into the familiar framework of integrable system
s with nondegenerate singularities\, and hence are
studied as a sort of edge case.\n\nIt is known th
at the fibers of these systems are determined as i
terated pullbacks by the combinatorics of joint ei
genvalues of systems of truncated matrices\, but t
he resulting expressions can be rather inexplicit.
We provide a new interpretation of Gelfand–Zeitli
n fibers as balanced products of Lie groups (or bi
quotients)\, and pursue these viewpoints to a dete
rmination of their cohomology rings and low-dimens
ional homotopy groups which can be read transparen
tly off of the combinatorics.\n\nThis all represen
ts joint work with Jeremy Lane.
LOCATION:MR13
CONTACT:Ivan Smith
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