Instanton Floer homology of almost-rational plumbings

Alfieri, Antonio¹ ; Baldwin, John A² ; Dai, Irving³ ; Sivek, Steven⁴

¹ Department of Mathematics, University of British Columbia, Vancouver, BC, Canada
² Department of Mathematics, Boston College, Chestnut Hill, MA, United States
³ Department of Mathematics, Stanford University, Stanford, CA, United States
⁴ Department of Mathematics, Imperial College London, London, United Kingdom, Max Planck Institute for Mathematics, Bonn, Germany

Geometry & topology, Tome 26 (2022) no. 5, pp. 2237-2294.

Résumé

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 $\widehat{HF}(Y;ℂ)$. 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 — with base ${ℝ\mathbb{P}}^2$ — directly). Our proof utilizes lattice homology, and relies on a decomposition theorem for instanton Floer cobordism maps recently established by Baldwin and Sivek.

Détail

DOI : 10.2140/gt.2022.26.2237

Keywords: instanton Floer homology, Heegaard Floer homology, lattice homology, plumbings

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