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Mathematical Research Letters
Volume 27 (2020)
Number 1
Mazur-type manifolds with $L$-space boundary
Pages: 35 – 42
DOI: https://dx.doi.org/10.4310/MRL.2020.v27.n1.a3
Authors
Abstract
In this note, we prove that if the boundary of a Mazur-type $4$‑manifold is an irreducible Heegaard Floer homology $L$‑space, then the manifold must be the $4$‑ball, and the boundary must be the $3$‑sphere. We use this to give a new proof of Gabai’s Property $\mathrm{R}$.
The first author was partially supported by NSF grant DMS-1344991 and the second author was partially supported by the Simons Foundation grant 636841, BT.
Received 6 August 2018
Accepted 10 February 2019
Published 8 April 2020