Power maps and principal bundles

Noakes, J. L.

doi:10.1090/S0002-9939-1977-0451245-3

Power maps and principal bundles
HTML articles powered by AMS MathViewer

by J. L. Noakes

Proc. Amer. Math. Soc. 64 (1977), 346-350

DOI: https://doi.org/10.1090/S0002-9939-1977-0451245-3

PDF | Request permission

Abstract:

Let G be a path connected topological group. We investigate the integers m for which the mth power map on G extends to an overmap of principal G-bundles.

References

A. K. Bousfield and D. M. Kan, Homotopy limits, completions and localizations, Lecture Notes in Mathematics, Vol. 304, Springer-Verlag, Berlin-New York, 1972. MR 0365573
Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–255. MR 155330, DOI 10.2307/1970341
I. M. James, Overhomotopy theory, Symposia Mathematica, Vol. IV (INDAM, Rome, 1968/69) Academic Press, London, 1970, pp. 219–229. MR 0275426

Some topics in homotopy theory

J. L. Noakes, Symmetric overmaps, Proc. Amer. Math. Soc. 56 (1976), 333–336. MR 405408, DOI 10.1090/S0002-9939-1976-0405408-2
J. L. Noakes, Unstable $J$-invariants, Quart. J. Math. Oxford Ser. (2) 27 (1976), no. 105, 51–57. MR 394656, DOI 10.1093/qmath/27.1.51
Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto-London, 1966. MR 0210112
Norman Steenrod, The Topology of Fibre Bundles, Princeton Mathematical Series, vol. 14, Princeton University Press, Princeton, N. J., 1951. MR 0039258
N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133–152. MR 210075