On -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

DOI:
https://doi.org/10.1090/S0002-9939-99-04637-7

Published electronically:
January 29, 1999

MathSciNet review:
1473672

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Abstract: Given a manifold of dimension at least 4 whose universal covering is homeomorphic to a sphere, the main result states that a compact manifold is isomorphic to a cylinder if and only if is homotopy equivalent to this cylinder and the boundary is isomorphic to two copies of ; this holds in the smooth, PL and topological categories. The result yields a classification of smooth, finite group actions on homotopy spheres (in dimensions ) 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:
https://doi.org/10.1090/S0002-9939-99-04637-7

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