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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Exact Calabi-Yau structures and disjoint Lagrangia
n spheres - Yin Li\, UCL
DTSTART;TZID=Europe/London:20191023T160000
DTEND;TZID=Europe/London:20191023T170000
UID:TALK125725AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/125725
DESCRIPTION:An exact CY structure is a special kind of smooth
CY structure in the sense of Kontsevich-Vlassopoul
os. When the wrapped Fukaya category of a Weinstei
n manifold admits an exact CY structure\, there is
an induced cohomology class in its 1st degree S^1
-equivariant symplectic cohomology\, which\, under
the marking map\, goes to an invertible element i
n the deg 0 (ordinary) symplectic cohomology. This
generalizes the notion of a (quasi-) dilation int
roduced earlier by Seidel-Solomon. \nWe show that
one can define q-intersection numbers between simp
ly-connected Lagrangian submanifolds in Weinstein
manifolds with exact CY wrapped Fukaya categories
and prove that there can be only finitely many dis
joint Lagrangian spheres in these manifolds.\nThe
simplest non-trivial example of a Weinstein manifo
ld whose wrapped Fukaya category is exact CY but w
hich does not admit a quasi-dilation is the Milnor
fiber of a 3-fold triple point studied previously
by Smith-Thomas.\n
LOCATION:MR13
CONTACT:Ivan Smith
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