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Proceedings of the American Mathematical Society

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

 

 

On the $ n$-parameter concordance and isotopy theorem


Author: Tadatoshi Akiba
Journal: Proc. Amer. Math. Soc. 61 (1976), 122-130
MSC: Primary 57C35
DOI: https://doi.org/10.1090/S0002-9939-1976-0433463-2
MathSciNet review: 0433463
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Abstract: J. F. P. Hudson [4] proved that ``concordance'' implies ``isotopy". In this paper we show that the $ n$-parameter version of Hudson's result cannot be true without some restrictions. Assuming Millett's result [6], we can determine a specific dimension where the $ n$-parameter version fails. We rely on Kan fibrations and geometric techniques such as the Alexander trick.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0433463-2
Keywords: $ k$-isotopy, semisimplicial complex, Alexander trick, fibration
Article copyright: © Copyright 1976 American Mathematical Society