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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Knots with Heegaard genus $ 2$ complements are invertible


Author: Richard P. Osborne
Journal: Proc. Amer. Math. Soc. 81 (1981), 501-502
MSC: Primary 57M25
DOI: https://doi.org/10.1090/S0002-9939-1981-0597671-4
MathSciNet review: 597671
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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 \mathop N\limits^ \circ (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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DOI: https://doi.org/10.1090/S0002-9939-1981-0597671-4
Article copyright: © Copyright 1981 American Mathematical Society