Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1979-0532158-7
MathSciNet review: 532158
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • [1] A. Casson and D. H. Gottlieb, Fibrations with compact fibres, Amer. J. Math. 99 (1977), 159-189. MR 0436144 (55:9094)
  • [2] P. Gabriel and M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Math. Wissenschaften, Springer-Verlag, Berlin, 1967. MR 0210125 (35:1019)
  • [3] S. M. Gersten, A product formula for Wall's obstruction, Amer. J. Math. 88 (1966), 337-346. MR 0198465 (33:6623)
  • [4] F. E. A. Johnson, Manifolds of homotopy type $ K(\pi ,1)$. I, Proc. Cambridge Philos. Soc. 70 (1971), 387-393. MR 0290358 (44:7542)
  • [5] J. P. Serre, Cohomologie des groupes discrets, Prospects in Mathematics, Ann. of Math. Studies, no. 70, Princeton University Press, Princeton, NJ., 1971, pp. 77-169. MR 0385006 (52:5876)
  • [6] J. R. Stallings, The piecewise-linear structure of Euclidean space, Proc. Cambridge Philos. Soc. 58 (1962), 481-487. MR 0149457 (26:6945)
  • [7] -, On finite processes leading to differentiability in the complement of a point, Differential and Combinatorial Topology, Princeton University Press, Princeton, NJ., 1965. MR 0180983 (31:5213)
  • [8] R. G. Swan, Periodic resolutions for finite groups, Ann. of Math. (2) 72 (1960), 267-291. MR 0124895 (23:A2205)
  • [9] J. H. C. Whitehead, Simplicial spaces, nuclei, and m-groups, Proc. London Math. Soc. 45 (1939), 243-337.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 57S30, 20J05

Retrieve articles in all journals with MSC: 57S30, 20J05


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1979-0532158-7
Keywords: Group of type VFP, periodic Farrell cohomology, fibre smoothing theorem, free proper discontinuous action
Article copyright: © Copyright 1979 American Mathematical Society

American Mathematical Society