A Functorial Symplectic Instanton Homology via Traceless Character Varieties
Location: Hill 525
Date & time: Tuesday, 25 October 2016 at 3:30PM - 3:31PM
Henry Horton, Indiana University: The Atiyah-Floer conjecture is the philosophy that gauge-theoretic Floer homology theories for 3-manifolds should be equivalently described by some Lagrangian Floer theory arising from Heegaard splittings. For Floer's original instanton homology (constructed from the Chern-Simons functional), the natural Lagrangian Floer theory to consider takes place in the SU(2)-character variety of the Heegaard surface and is not well-defined due to singularities arising from reducible representations. Nearly a decade ago, Kronheimer and Mrowka defined a framed instanton homology' for which all critical points of the associated Chern-Simons functional correspond to irreducible SU(2) representations. In this talk, we explain our approach to constructing an elementary Lagrangian Floer theory which conjecturally agrees with the framed instanton homology. Furthermore, we will describe how cobordisms of 3-manifolds induce homomorphisms between the so-called 'symplectic instanton homology' groups on the two ends and discuss other structural properties of this invariant.'