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Null-homotopic knots have Property R

Published online by Cambridge University Press:  20 February 2023

YI NI
YI NI*
Affiliation:
Department of Mathematics, California Institute of Technology, MC 253-37, 1200 E California Blvd, Pasadena, CA 91206, U.S.A. e-mail: yini@caltech.edu
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Abstract

We prove that if K is a nontrivial null-homotopic knot in a closed oriented 3–manfiold Y such that $Y-K$ does not have an $S^1\times S^2$ summand, then the zero surgery on K does not have an $S^1\times S^2$ summand. This generalises a result of Hom and Lidman, who proved the case when Y is an irreducible rational homology sphere.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 175 , Issue 1 , July 2023 , pp. 217 - 223
Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Cambridge Philosophical Society

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