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Instanton Floer homology of almost-rational plumbings

### Antonio Alfieri, John A Baldwin, Irving Dai and Steven Sivek

Geometry & Topology 26 (2022) 2237–2294
##### Abstract

We show that if $Y$ is the boundary of an almost-rational plumbing, then the framed instanton Floer homology ${I}^{#}\left(Y\right)$ is isomorphic to the Heegaard Floer homology $\stackrel{^}{HF}\left(Y;ℂ\right)$. This class of $3$–manifolds includes all Seifert fibered rational homology spheres with base orbifold ${S}^{2}$ (we establish the isomorphism for the remaining Seifert fibered rational homology spheres — with base ${ℝℙ}^{2}$ — directly). Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps recently established by Baldwin and Sivek.

##### Keywords
instanton Floer homology, Heegaard Floer homology, lattice homology, plumbings
Primary: 57R58