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On spaces with periodic cohomology
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On spaces with periodic cohomology
Alejandro Adem and Jeff H. Smith
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.
Copyright 2000 American Mathematical Society
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Article Info
- ERA Amer. Math. Soc. 06 (2000), pp. 1-6
- Publisher Identifier: S 1079-6762(00)00074-3
- 2000 Mathematics Subject Classification. Primary 57S30; Secondary 20J06
- Key words and phrases. Group cohomology, periodic complex
- Received by the editors October 27, 1999
- Posted on January 31, 2000
- Communicated by Dave J. Benson
- Comments (When Available)
Alejandro Adem
Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706
E-mail address: adem@math.wisc.edu
Jeff H. Smith
Mathematics Department, Purdue University, West Lafayette, Indiana 47907
E-mail address: jhs@math.purdue.edu
Both authors were partially supported by grants from the NSF
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