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Homology spheres and property R

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arxiv 1906.11234 v2 pith:6HRRPH6J submitted 2019-06-26 math.GT

Min Hoon Kim , JungHwan Park This is my paper · ORCID
classification math.GT
keywords homologyspherescontaindistinctinfinitelykirbyknotsmany
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abstract

We present infinitely many homology spheres which contain two distinct knots whose 0-surgeries are $S^1 \times S^2$. This resolves a question posed by Kirby and Melvin in 1978.

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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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