UBC Topology Seminar: Antonio Alfieri (Online)

Plumbed three-manifolds are those three-manifolds that can be be realized 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.