Null-homotopic knots have Property R

IF 0.6 3区数学 Q3 MATHEMATICS

Mathematical Proceedings of the Cambridge Philosophical Society Pub Date : 2022-01-25 DOI:10.1017/S0305004123000129

Yi Ni

引用次数: 0

Abstract

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.

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零同伦结有性质R

摘要证明了如果K是一个非平凡的零同伦结，使得$Y-K$不存在$S^1\ * S^2$和，则K上的零点手术不存在$S^1\ * S^2$和。这推广了Hom和Lidman的结果，他们证明了Y是不可约有理同调球的情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Proceedings of the Cambridge Philosophical Society 数学-数学

CiteScore

1.70

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Papers which advance knowledge of mathematics, either pure or applied, will be considered by the Editorial Committee. The work must be original and not submitted to another journal.