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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

A relative Nash theorem


Authors: Selman Akbulut and Henry C. King
Journal: Trans. Amer. Math. Soc. 267 (1981), 465-481
MSC: Primary 58A07; Secondary 14G30, 57R99
DOI: https://doi.org/10.1090/S0002-9947-1981-0626484-4
MathSciNet review: 626484
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Abstract: We prove that if $ M$ is a closed smooth manifold and $ {M_i}$, $ i = 1, \ldots ,k$, are transversally intersecting closed smooth submanifolds of $ M$, then there exist a nonsingular algebraic set $ Z$ and nonsingular algebraic subsets $ {Z_i}$, $ i = 1, \ldots ,k$, of $ Z$ such that $ (M;{M_1}, \ldots ,{M_k})$ is diffeomorphic to $ (Z;{Z_1}, \ldots ,{Z_k})$. We discuss a generalization and the consequences of this result.


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DOI: https://doi.org/10.1090/S0002-9947-1981-0626484-4
Article copyright: © Copyright 1981 American Mathematical Society