A Concordance Extension Theorem

Author:
Joel L. Jones

Journal:
Trans. Amer. Math. Soc. **348** (1996), 205-218

MSC (1991):
Primary 57N37; Secondary 55R65, 57N70

MathSciNet review:
1303122

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Abstract: Let be a manifold approximate fibration between closed manifolds, where , and let be the mapping cylinder of . In this paper it is shown that if is any concordance on , then there exists a concordance such that and . As an application, if and are closed manifolds where is a locally flat submanifold of and and , then a concordance extends to a concordance on such that . This uses the fact that under these hypotheses there exists a manifold approximate fibration , where is a closed -manifold, such that the mapping cylinder is homeomorphic to a closed neighborhood of in by a homeomorphism which is the identity on .

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Additional Information

**Joel L. Jones**

Affiliation:
Department of Mathematics, Presbyterian College, Clinton, South Carolina 29325

Email:
jjones@cs1.presby.edu

DOI:
https://doi.org/10.1090/S0002-9947-96-01378-5

Keywords:
Concordance,
manifold approximate fibration,
mapping cylinder

Received by editor(s):
October 31, 1994

Article copyright:
© Copyright 1996
American Mathematical Society