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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#(Y ) is isomorphic to the Heegaard Floer homology HF^(Y ; ). This class of 3–manifolds includes all Seifert fibered rational homology spheres with base orbifold S2 (we establish the isomorphism for the remaining Seifert fibered rational homology spheres — with base 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
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