Instanton Floer homology of almost-rational plumbings

Alfieri, Antonio; Baldwin, John A; Dai, Irving; Sivek, Steven

doi:10.2140/gt.2022.26.2237

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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

DOI: 10.2140/gt.2022.26.2237

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

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Keywords

instanton Floer homology, Heegaard Floer homology, lattice homology, plumbings

Mathematical Subject Classification

Primary: 57R58

References

Publication

Received: 13 October 2020

Revised: 4 May 2021

Accepted: 4 June 2021

Published: 12 December 2022

Proposed: Ciprian Manolescu

Seconded: András I Stipsicz, Simon Donaldson

Authors

Antonio Alfieri
Department of Mathematics University of British Columbia Vancouver, BC Canada

John A Baldwin
Department of Mathematics Boston College Chestnut Hill, MA United States

Irving Dai
Department of Mathematics Stanford University Stanford, CA United States

Steven Sivek
Department of Mathematics Imperial College London London United Kingdom	Max Planck Institute for Mathematics Bonn Germany

Volume 26, issue 5 (2022)