Antonio Alfieri (UBC)

Title: Instanton Floer homology of almost-rational plumbings

Abstract: Plumbed three-manifolds are those three-manifolds that can
be be realised as links of isolated complex surface
singularities. Inspired by Heegaard Floer theory, Nemethi introduced a
combinatorial invariant of complex surface singularities (lattice
cohomology) that is conjectured to be isomorphic to Heegaard Floer
homology. I will expose some recent work in collaboration with John
Baldwin, Irving Dai, and Steven Sivek showing that the lattice
cohomology of an almost-rational singularity is isomorphic to the
framed instanton Floer homology of its link. The proof goes through
lattice cohomology and makes use of the decomposition along
characteristic vectors of the instanton cobordism maps recently found
by Baldwin and Sivek.