Mathematical Research Letters

Volume 27 (2020)

Number 1

Mazur-type manifolds with $L$-space boundary

Pages: 35 – 42



James Conway (Department of Mathematics, University of California at Berkeley)

Bülent Tosun (Department of Mathematics, University of Alabama, Tuscaloosa, Al, U.S.A.)


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