𝑘-invariants in local coefficient theory

Siegel, Jerrold

doi:10.1090/S0002-9939-1971-0307224-4

$k$-invariants in local coefficient theory
HTML articles powered by AMS MathViewer

by Jerrold Siegel PDF

Proc. Amer. Math. Soc. 29 (1971), 169-174 Request permission

Abstract:

A transgression-obstruction theorem is presented for not necessarily simply connected spaces. This theorem is used to produce an explicit model for a classifying space for fibre homotopy equivalence classes of fibrations with fibre a $K(\pi ,n)$.

References

Guy Allaud, On the classification of fiber spaces, Math. Z. 92 (1966), 110–125. MR 189035, DOI 10.1007/BF01312430
Albrecht Dold, Partitions of unity in the theory of fibrations, Ann. of Math. (2) 78 (1963), 223–255. MR 155330, DOI 10.2307/1970341
Albrecht Dold, Halbexakte Homotopiefunktoren, Lecture Notes in Mathematics, vol. 12, Springer-Verlag, Berlin-New York, 1966 (German). MR 0198464
Daniel H. Gottlieb, On fibre spaces and the evaluation map, Ann. of Math. (2) 87 (1968), 42–55. MR 221508, DOI 10.2307/1970593
William Huebsch, On the covering homotopy theorem, Ann. of Math. (2) 61 (1955), 555–563. MR 91470, DOI 10.2307/1969813
James F. McClendon, Obstruction theory in fiber spaces, Math. Z. 120 (1971), 1–17. MR 296943, DOI 10.1007/BF01109713
Jerrold Siegel, Higher order cohomology operations in local coefficient theory, Amer. J. Math. 89 (1967), 909–931. MR 225319, DOI 10.2307/2373410
Jerrold Siegel, Cohomology operations in local coefficient theory, Illinois J. Math. 15 (1971), 52–63. MR 270365
James Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246. MR 154286, DOI 10.1016/0040-9383(63)90006-5