Department of Mathematics

Geometry and Topology

  •  Towards extended Floer field theories
  •  02/01/2018
  •  2:00 PM - 2:50 PM
  •  C304 Wells Hall
  •  Guillem Cazassus, Indiana University

Donaldson polynomials are powerful invariants associated to smooth four-manifolds. The introduction by Floer of Instanton homology groups, associated to some 3-manifolds, allowed to define analogs of such polynomials for (some) four-manifolds with boundary, that have a structure similar with a TQFT. Wehrheim and Woodward developed a framework called "Floer field theory" which, according to the Atiyah-Floer conjecture, should permit to recover Donaldson invariants from a 2-functor from the 2-category Cob_{2+1+1} to a 2-category Symp they defined, which is an enrichment of Weinstein's symplectic category. I will describe a framework that should permit to extend such a 2-functor to lower dimensions. This framework should permit to define new invariants in Manolescu and Woodward's symplectic instanton homology (sutured theory, equivariant version). This is work in progress.

 

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