×

Approximating groups of bundle automorphisms by loop spaces. (English) Zbl 0519.55011

MSC:

55R10 Fiber bundles in algebraic topology
55P10 Homotopy equivalences in algebraic topology
55P35 Loop spaces
54C35 Function spaces in general topology
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Peter I. Booth and Ronald Brown, Spaces of partial maps, fibred mapping spaces and the compact-open topology, General Topology and Appl. 8 (1978), no. 2, 181 – 195. Peter I. Booth and Ronald Brown, On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps, General Topology and Appl. 8 (1978), no. 2, 165 – 179. · Zbl 0373.54012
[2] Peter I. Booth and Ronald Brown, Spaces of partial maps, fibred mapping spaces and the compact-open topology, General Topology and Appl. 8 (1978), no. 2, 181 – 195. Peter I. Booth and Ronald Brown, On the application of fibred mapping spaces to exponential laws for bundles, ex-spaces and other categories of maps, General Topology and Appl. 8 (1978), no. 2, 165 – 179. · Zbl 0373.54012
[3] P. I. Booth et al., \( H\)-spaces of self-equivalences of fibrations and bundles (preprint). · Zbl 0525.55005
[4] Ronald Brown and Philip R. Heath, Coglueing homotopy equivalences, Math. Z. 113 (1970), 313 – 325. · Zbl 0185.51101 · doi:10.1007/BF01110331
[5] Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223 – 255. · Zbl 0203.25402 · doi:10.2307/1970341
[6] Daniel Henry Gottlieb, Applications of bundle map theory, Trans. Amer. Math. Soc. 171 (1972), 23 – 50. · Zbl 0251.55018
[7] Dale Husemoller, Fibre bundles, 2nd ed., Springer-Verlag, New York-Heidelberg, 1975. Graduate Texts in Mathematics, No. 20. · Zbl 0307.55015
[8] I. M. James, The space of bundle maps, Topology 2 (1963), 45 – 59. · Zbl 0114.39904 · doi:10.1016/0040-9383(63)90021-1
[9] S. S. Koh, Note on the homotopy properties of the components of the mapping space \?^{\?^{\?}}, Proc. Amer. Math. Soc. 11 (1960), 896 – 904. · Zbl 0097.16103
[10] John Milnor, Construction of universal bundles. I, Ann. of Math. (2) 63 (1956), 272 – 284. · Zbl 0071.17302 · doi:10.2307/1969609
[11] John Milnor, Construction of universal bundles. II, Ann. of Math. (2) 63 (1956), 430 – 436. · Zbl 0071.17401 · doi:10.2307/1970012
[12] C. Morgan, \( F\)-fibrations and groups of gauge transformations, Ph.D. Thesis, Memorial Univ. of Newfoundland, 1980.
[13] Rolf Schön, Fibrations over a CWh-base, Proc. Amer. Math. Soc. 62 (1976), no. 1, 165 – 166 (1977). · Zbl 0346.55020
[14] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1966. · Zbl 0145.43303
[15] A. Trautman, Fibre bundles associated with space-time, Rep. Mathematical Phys. 1 (1970/1971), no. 1, 29 – 62. · Zbl 0204.29802
[16] Andrzej Trautman, On groups of gauge transformations, Geometrical and topological methods in gauge theories (Proc. Canad. Math. Soc. Summer Res. Inst., McGill Univ., Montreal, Que., 1979) Lecture Notes in Phys., vol. 129, Springer, Berlin-New York, 1980, pp. 114 – 120. · Zbl 0447.53061
[17] Rainer M. Vogt, Convenient categories of topological spaces for homotopy theory, Arch. Math. (Basel) 22 (1971), 545 – 555. · Zbl 0237.54001 · doi:10.1007/BF01222616
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.