Some function spaces of CW type

Kahn, Peter J.

doi:10.1090/S0002-9939-1984-0733413-X

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Some function spaces of CW type

Author: Peter J. Kahn
Journal: Proc. Amer. Math. Soc. 90 (1984), 599-607
MSC: Primary 55P99; Secondary 54E60
MathSciNet review: 733413
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Abstract: J. Milnor's result on the CW type of certain function spaces ${\operatorname{map}}\left( {X,Y} \right)$ is extended to allow the case in which has a finite -skeleton and ${\pi _i}Y = 0$ , . One conclusion is that the self-equivalence monoid of any Postnikov stage of a finite complex has CW type. Another is that the monoid of pointed self-equivalences of a $K\left( {\pi ,1} \right)$ manifold has contractible components when $\pi$ is finitely-generated.

[1] Kenneth S. Brown, Cohomology of groups, Graduate Texts in Mathematics, vol. 87, Springer-Verlag, New York, 1982. MR 672956 (83k:20002)
[2] Albrecht Dold, Halbexakte Homotopiefunktoren, Lecture Notes in Mathematics, vol. 12, Springer-Verlag, Berlin, 1966 (German). MR 0198464 (33 #6622)
[3] Albrecht Dold and Richard Lashof, Principal quasi-fibrations and fibre homotopy equivalence of bundles., Illinois J. Math. 3 (1959), 285–305. MR 0101521 (21 #331)
[4] Martin Fuchs, A modified Dold-Lashof construction that does classify 𝐻-principal fibrations, Math. Ann. 192 (1971), 328–340. MR 0292080 (45 #1167)
[5] Martin Fuchs, The functor [,𝑌] and loop fibrations. I, Michigan Math. J. 14 (1967), 283–287. MR 0217794 (36 #883)
[6] P. J. Hilton, Homotopy theory and duality, Gordon & Breach, New York, 1966.
[7] A. Lundell and S. Weingram, The topology of CW complexes, Van Nostrand, Princeton, N. J., 1969.
[8] J. Peter May, Simplicial objects in algebraic topology, Van Nostrand Mathematical Studies, No. 11, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0222892 (36 #5942)
[9] John Milnor, On spaces having the homotopy type of a 𝐶𝑊-complex, Trans. Amer. Math. Soc. 90 (1959), 272–280. MR 0100267 (20 #6700), http://dx.doi.org/10.1090/S0002-9947-1959-0100267-4
[10] Yasutoshi Nomura, On extensions of triads, Nagoya Math. J. 27 (1966), 249–277. MR 0203732 (34 #3581)
[11] Edwin H. Spanier, Algebraic topology, McGraw-Hill Book Co., New York, 1966. MR 0210112 (35 #1007)
[12] James Stasheff, A classification theorem for fibre spaces, Topology 2 (1963), 239–246. MR 0154286 (27 #4235)
[13] James Stasheff, 𝐻-spaces from a homotopy point of view, Lecture Notes in Mathematics, Vol. 161, Springer-Verlag, Berlin, 1970. MR 0270372 (42 #5261)
[14] N. E. Steenrod, A convenient category of topological spaces, Michigan Math. J. 14 (1967), 133–152. MR 0210075 (35 #970)
[15] R. Thom, L’homologie des espaces fonctionnels, Colloque de topologie algébrique, Louvain, 1956, Georges Thone, Liège, 1957, pp. 29–39 (French). MR 0089408 (19,669h)
[16] C. T. C. Wall, Finiteness conditions for 𝐶𝑊-complexes, Ann. of Math. (2) 81 (1965), 56–69. MR 0171284 (30 #1515)
[17] C. T. C. Wall, Finiteness conditions for 𝐶𝑊 complexes. II, Proc. Roy. Soc. Ser. A 295 (1966), 129–139. MR 0211402 (35 #2283)
[18] Topology of manifolds, Proceedings of the University of Georgia Topology of Manifolds Institute, vol. 1969, Markham Publishing Co., Chicago, Ill., 1970. MR 0268896 (42 #3793)

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