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On groups which act freely on vector bundles over spheres

Author: F. E. A. Johnson
Journal: Proc. Amer. Math. Soc. 75 (1979), 318-320
MSC: Primary 57S30; Secondary 20J05
MathSciNet review: 532158
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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.

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  • [1] Andrew Casson and Daniel Henry Gottlieb, Fibrations with compact fibres, Amer. J. Math. 99 (1977), no. 1, 159–189. MR 0436144
  • [2] 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
  • [3] Stephen M. Gersten, A product formula for Wall’s obstruction, Amer. J. Math. 88 (1966), 337–346. MR 0198465
  • [4] F. E. A. Johnson, Manifolds of homotopy type 𝐾(𝜋,1). I, Proc. Cambridge Philos. Soc. 70 (1971), 387–393. MR 0290358
  • [5] Jean-Pierre Serre, Cohomologie des groupes discrets, Prospects in mathematics (Proc. Sympos., Princeton Univ., Princeton, N.J., 1970) Princeton Univ. Press, Princeton, N.J., 1971, pp. 77–169. Ann. of Math. Studies, No. 70 (French). MR 0385006
  • [6] John Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481–488. MR 0149457
  • [7] 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
  • [8] Richard G. Swan, Periodic resolutions for finite groups, Ann. of Math. (2) 72 (1960), 267–291. MR 0124895
  • [9] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. 45 (1939), 243-337.

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Keywords: Group of type VFP, periodic Farrell cohomology, fibre smoothing theorem, free proper discontinuous action
Article copyright: © Copyright 1979 American Mathematical Society