Geodesic
On spaces with periodic cohomology
Adem, Alejandro1 ; Smith, Jeff2
1Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706
2Mathematics Department, Purdue University, West Lafayette, Indiana 47907
Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 1-6
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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.
DOI : 10.1090/S1079-6762-00-00074-3

Adem, Alejandro  1   ; Smith, Jeff  2

1 Mathematics Department, University of Wisconsin, Madison, Wisconsin 53706
2 Mathematics Department, Purdue University, West Lafayette, Indiana 47907 
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Adem, Alejandro; Smith, Jeff. On spaces with periodic cohomology. Electronic research announcements of the American Mathematical Society, Tome 06 (2000), pp. 1-6. doi: 10.1090/S1079-6762-00-00074-3

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