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ISSN 1079-6762

 

On spaces with periodic cohomology


Authors: Alejandro Adem and Jeff H. Smith
Journal: Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 1-6
MSC (2000): Primary 57S30; Secondary 20J06
Published electronically: January 31, 2000
MathSciNet review: 1745517
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Abstract:

We define a generalized notion of cohomological periodicity for a connected CW-complex $X$, and show that it is equivalent to the existence of an oriented spherical fibration over $X$with total space homotopy equivalent to a finite dimensional complex. As applications we characterize discrete groups which can act freely and properly on some $\mathbb R^n\times \mathbb S^m$, show that every rank two $p$-group acts freely on a homotopy product of two spheres and construct exotic free actions of many simple groups on such spaces.


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Additional Information

Alejandro Adem
Affiliation: Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706
Email: adem@math.wisc.edu

Jeff H. Smith
Affiliation: Mathematics Department, Purdue University, West Lafayette, Indiana 47907
Email: jhs@math.purdue.edu

DOI: http://dx.doi.org/10.1090/S1079-6762-00-00074-3
PII: S 1079-6762(00)00074-3
Keywords: Group cohomology, periodic complex
Received by editor(s): October 27, 1999
Published electronically: January 31, 2000
Additional Notes: Both authors were partially supported by grants from the NSF
Communicated by: Dave J. Benson
Article copyright: © Copyright 2000 American Mathematical Society