Knots with Heegaard genus 2 complements are invertible

Osborne, Richard P.

doi:10.1090/S0002-9939-1981-0597671-4

Knots with Heegaard genus $2$ complements are invertible
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by Richard P. Osborne

Proc. Amer. Math. Soc. 81 (1981), 501-502

DOI: https://doi.org/10.1090/S0002-9939-1981-0597671-4

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Abstract:

Let $K$ be a polyhedral oriented knot in ${S^3}$ and $N(K)$ be a regular neighborhood of $K$. If ${S^3} \sim \mathring {N} (K)$ can be constructed by attaching a single $2$-handle to a genus two handlebody, then there is a homeomorphism of ${S^3}$ onto itself mapping $K$ onto itself and reversing the orientation of $K$.

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