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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Lagrangian cobordisms and K-theory of bielliptic s
urfaces - Álvaro Muñiz Brea (Edinburgh)
DTSTART;TZID=Europe/London:20240313T160000
DTEND;TZID=Europe/London:20240313T170000
UID:TALK209017AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/209017
DESCRIPTION:The Lagrangian cobordism group is a topological i
nvariant of a symplectic manifold which encodes in
formation about the triangulated structure of its
Fukaya category (in the sense that it admits a hom
omorphism onto the Grothendieck group of the latte
r). In the lowest dimensional case of Riemann surf
aces this map is an isomorphism\, so the cobordism
group `sees all of the triangulated structure'\;
whether this is the case in higher dimensions is a
n open problem. Recent results of Sheridan-Smith s
how that Lagrangian cobordism groups of symplectic
4-manifolds with trivial canonical bundle are so
large and complicated as to make a direct computat
ion unfeasible. In this talk I will consider a sym
plectic 4-manifold whose canonical bundle is torsi
on but not trivial\, and explain that (a certain s
ubgroup of) the cobordism group can be directly co
mputed in this case. Then\, using homologicla mirr
or symmetry and the computation of the Chow groups
of the mirror variety\, I will show that this sub
group maps isomorphically onto the Grothendieck gr
oup of the Fukaya category.
LOCATION:MR13
CONTACT:Oscar Randal-Williams
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