Instanton Floer homology of almost-rational plumbings

Abstract

We show that if $Y$ is the boundary of an almost-rational plumbing, then the framed instanton Floer homology $I^{\#}(Y)$ is isomorphic to the Heegaard Floer homology $\widehat{HF}(Y;\mathbb{C})$. 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$\unicode{x2014}$with base ${\mathbb{RP}}^2$$\unicode{x2014}$directly). Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps recently established by Baldwin and Sivek.

41 pages, 9 figures; fixed minor typos, to appear in Geometry & Topology

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Cited by in corpus (5)

• Instanton Floer homology, sutures, and Heegaard diagrams
• Instanton L-spaces and splicing
• Knot surgery formulae for instanton Floer homology II: applications
• SU(2) representations and a large surgery formula
• Deformations of lattice cohomology and the upsilon invariant