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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Floer theoretically essential tori in rational blo
wdowns - Yankl Lekili\, Cambridge
DTSTART;TZID=Europe/London:20120314T160000
DTEND;TZID=Europe/London:20120314T173000
UID:TALK35257AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/35257
DESCRIPTION:We compute the Floer cohomology of monotone tori i
n the Stein surface obtained by a linear plumbing
of cotangent bundles of spheres\, also known as th
e Milnor fibre associated with the complex surface
\nsingularity of type A-n. We next study some fini
te quotients of the A-n Milnor fibre which coincid
e with the Stein surfaces that appear in Fintushel
and Stern's rational blowdown construction. We sh
ow that these\nStein surfaces have no exact Lagran
gian submanifolds by using the already available a
nd in depth understanding of the Fukaya category o
f the A-n Milnor fibre coming from homological mir
ror symmetry. On the\ncontrary\, we find Floer the
oretically essential monotone Lagrangian tori\, fi
nitely covered by the monotone tori that we studie
d in the A-n\nMilnor fibre. We conclude that these
Stein surfaces have non-vanishing symplectic coho
mology. Joint work with Maksim Maydanskiy.
LOCATION:MR13
CONTACT:Ivan Smith
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