On spaces with periodic cohomology
Authors:
Alejandro Adem and Jeff H. Smith
Journal:
Electron. Res. Announc. Amer. Math. Soc. 6 (2000), 16
MSC (2000):
Primary 57S30; Secondary 20J06
Published electronically:
January 31, 2000
MathSciNet review:
1745517
Fulltext PDF Free Access
Abstract 
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Abstract: We define a generalized notion of cohomological periodicity for a connected CWcomplex , and show that it is equivalent to the existence of an oriented spherical fibration over with total space homotopy equivalent to a finite dimensional complex. As applications we characterize discrete groups which can act freely and properly on some , show that every rank two 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/S1079676200000743
PII:
S 10796762(00)000743
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
