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SUMMARY:Floer theoretically essential tori in rational blowdowns - Yankl L
 ekili\, Cambridge
DTSTART:20120314T160000Z
DTEND:20120314T173000Z
UID:TALK35257@talks.cam.ac.uk
CONTACT:Ivan Smith
DESCRIPTION:We compute the Floer cohomology of monotone tori in the Stein 
 surface obtained by a linear plumbing of cotangent bundles of spheres\, al
 so known as the Milnor fibre associated with the complex surface\nsingular
 ity of type A-n. We next study some finite quotients of the A-n Milnor fib
 re which coincide with the Stein surfaces that appear in Fintushel and Ste
 rn's rational blowdown construction. We show that these\nStein surfaces ha
 ve no exact Lagrangian submanifolds by using the already available and in 
 depth understanding of the Fukaya category of the A-n Milnor fibre coming 
 from homological mirror symmetry. On the\ncontrary\, we find Floer theoret
 ically essential monotone Lagrangian tori\, finitely covered by the monoto
 ne tori that we studied in the A-n\nMilnor fibre. We conclude that these S
 tein surfaces have non-vanishing symplectic cohomology. Joint work with Ma
 ksim Maydanskiy.
LOCATION:MR13
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