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Transactions of the American Mathematical Society

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Controlled boundary and $ h$-cobordism theorems


Author: T. A. Chapman
Journal: Trans. Amer. Math. Soc. 280 (1983), 73-95
MSC: Primary 57R80; Secondary 57Q10
DOI: https://doi.org/10.1090/S0002-9947-1983-0712250-X
MathSciNet review: 712250
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Abstract: In this paper two theorems are established which are consequences of some earlier approximation results of the author. The first theorem is a controlled boundary theorem for finite-dimensional manifolds. By this we mean an ordinary boundary theorem plus small $ \varepsilon $-control in a given parameter space. The second theorem is a controlled $ h$-cobordism theorem for finite-dimensional manifolds with small $ \varepsilon $-control in a given parameter space. These results generalize the End Theorem and the Thin $ h$-Corbordism of Quinn.


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DOI: https://doi.org/10.1090/S0002-9947-1983-0712250-X
Keywords: Boundary theorem, $ h$-cobordism theorem
Article copyright: © Copyright 1983 American Mathematical Society

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