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SUMMARY:Lagrangian cobordisms and K-theory of bielliptic surfaces - Álvar
 o Muñiz Brea (Edinburgh)
DTSTART:20240313T160000Z
DTEND:20240313T170000Z
UID:TALK209017@talks.cam.ac.uk
CONTACT:Oscar Randal-Williams
DESCRIPTION:The Lagrangian cobordism group is a topological​ invariant o
 f a symplectic manifold which encodes information about the triangulated s
 tructure of its Fukaya category (in the sense that it admits a homomorphis
 m onto the Grothendieck group of the latter). In the lowest dimensional ca
 se of Riemann surfaces this map is an isomorphism\, so the cobordism group
  `sees all of the triangulated structure'\; whether this is the case in hi
 gher dimensions is an open problem. Recent results of Sheridan-Smith show 
 that Lagrangian cobordism groups of symplectic 4-manifolds with trivial ca
 nonical bundle are so large and complicated as to make a direct computatio
 n unfeasible. In this talk I will consider a symplectic 4-manifold whose c
 anonical bundle is torsion but not trivial\, and explain that (a certain s
 ubgroup of) the cobordism group can be directly computed in this case. The
 n\, using homologicla mirror symmetry and the computation of the Chow grou
 ps of the mirror variety\, I will show that this subgroup maps isomorphica
 lly onto the Grothendieck group of the Fukaya category. 
LOCATION:MR13
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