On groups which act freely on vector bundles over spheres

Johnson, F. E. A.

doi:10.1090/S0002-9939-1979-0532158-7

On groups which act freely on vector bundles over spheres
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by F. E. A. Johnson

Proc. Amer. Math. Soc. 75 (1979), 318-320

DOI: https://doi.org/10.1090/S0002-9939-1979-0532158-7

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Abstract:

Let $G \cong K \times Q$ be the semidirect product of a finitely presented group K of type FP and a finite group Q of periodic cohomology. It is shown that G acts freely and properly discontinuously on a vector bundle over a sphere.

References

Andrew Casson and Daniel Henry Gottlieb, Fibrations with compact fibres, Amer. J. Math. 99 (1977), no. 1, 159–189. MR 436144, DOI 10.2307/2374013
P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer-Verlag New York, Inc., New York, 1967. MR 0210125
Stephen M. Gersten, A product formula for Wall’s obstruction, Amer. J. Math. 88 (1966), 337–346. MR 198465, DOI 10.2307/2373197
F. E. A. Johnson, Manifolds of homotopy type $K(\pi ,\,1)$. I, Proc. Cambridge Philos. Soc. 70 (1971), 387–393. MR 290358, DOI 10.1017/s0305004100050003
Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) Ann. of Math. Studies, No. 70, Princeton Univ. Press, Princeton, N.J., 1971, pp. 77–169 (French). MR 0385006
John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481–488. MR 149457
John R. Stallings, On infinite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 245–254. MR 0180983
Richard G. Swan, Periodic resolutions for finite groups, Ann. of Math. (2) 72 (1960), 267–291. MR 124895, DOI 10.2307/1970135

Simplicial spaces, nuclei, and m-groups

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