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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Higher dimensional knots in tubes


Author: Yaichi Shinohara
Journal: Trans. Amer. Math. Soc. 161 (1971), 35-49
MSC: Primary 57.20; Secondary 55.00
MathSciNet review: 0287559
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Abstract: Let K be an n-knot in the $ (n + 2)$-sphere and V a tubular neighborhood of K. Let $ L'$ be an n-knot contained in a tubular neighborhood $ V'$ of a trivial n-knot and L the image of $ L'$ under an orientation preserving diffeomorphism of $ V'$ onto V. The purpose of this paper is to show that the higher dimensional Alexander polynomial and the signature of the n-knot L are determined by those of K and $ L'$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0287559-9
PII: S 0002-9947(1971)0287559-9
Keywords: qth dimensional Alexander polynomial, signature of n-knots
Article copyright: © Copyright 1971 American Mathematical Society