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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On $\mathit{h}$-cobordisms of spherical space forms


Authors: Slawomir Kwasik and Reinhard Schultz
Journal: Proc. Amer. Math. Soc. 127 (1999), 1525-1532
MSC (1991): Primary 57R80, 57S25
Published electronically: January 29, 1999
MathSciNet review: 1473672
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Abstract: Given a manifold $M$ of dimension at least 4 whose universal covering is homeomorphic to a sphere, the main result states that a compact manifold $W$ is isomorphic to a cylinder $M\times [0,1]$ if and only if $W$ is homotopy equivalent to this cylinder and the boundary is isomorphic to two copies of $M$; this holds in the smooth, PL and topological categories. The result yields a classification of smooth, finite group actions on homotopy spheres (in dimensions $\geq 5$) with exactly two singular points.


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Additional Information

Slawomir Kwasik
Affiliation: Department of Mathematics, Tulane University, New Orleans, Louisiana 70118
Email: kwasik@math.tulane.edu

Reinhard Schultz
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics, University of California, Riverside, California 92521
Email: schultz@math.ucr.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04637-7
PII: S 0002-9939(99)04637-7
Received by editor(s): June 23, 1997
Received by editor(s) in revised form: September 2, 1997
Published electronically: January 29, 1999
Additional Notes: The first author was partially supported by NSF Grant DMS 91-01575 and by a COR grant from Tulane University. The second author was partially supported by NSF grant DMS 91-02711.
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1999 American Mathematical Society