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.



Department of Mathematics
Michigan State University
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