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Mazur-type manifolds with $L$-space boundaries

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arxiv 1807.08880 v1 pith:3UKM4VIZ submitted 2018-07-24 math.GT math.SG

James Conway , Bülent Tosun This is my paper · ORCID
classification math.GTmath.SG
keywords boundarymanifoldmazur-typemustspaceballboundariesfloer
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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 R.

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  1. Exotic Mazur manifolds and knot trace invariants

    math.GT 2019-08 conditional novelty 8.0 of 10

    Exotic Mazur manifolds exist, and the knot Floer invariant ν is shown to be an invariant of knot traces, yielding counterexamples to a conjecture in Kirby's problem list.

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