Controlled boundary and -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 -control in a given parameter space. The second theorem is a controlled -cobordism theorem for finite-dimensional manifolds with small -control in a given parameter space. These results generalize the End Theorem and the Thin -Corbordism of Quinn.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1983-0712250-X

Keywords:
Boundary theorem,
-cobordism theorem

Article copyright:
© Copyright 1983
American Mathematical Society