New proofs of Chapman’s 𝐶𝐸 mapping theorem and West’s mapping cylinder theorem

New proofs of Chapman’s $\textrm {CE}$ mapping theorem and West’s mapping cylinder theorem
HTML articles powered by AMS MathViewer

by A. Fathi, A. Marin and Y. M. Visetti PDF

Proc. Amer. Math. Soc. 67 (1977), 327-334 Request permission

This note proves two theorems of the theory of Q-manifolds; the original proofs are simplified by using Bing shrinking criterion.

References

On cellular approximations of manifolds

Notes on Hilbert cube manifolds

T. A. Chapman, Cell-like mappings of Hilbert cube manifolds: solution of a handle problem, General Topology and Appl. 5 (1975), 123–145. MR 377894, DOI 10.1016/0016-660X(75)90017-3
T. A. Chapman, Cell-like mappings of Hilbert cube manifolds: applications to simple homotopy theory, Bull. Amer. Math. Soc. 79 (1973), 1286–1291. MR 326740, DOI 10.1090/S0002-9904-1973-13417-2

Siebenmann’s variation of West’s proof of the ANR theorem

The Bing staircase construction for Q-manifolds

William E. Haver, Mappings between $\textrm {ANR}$s that are fine homotopy equivalences, Pacific J. Math. 58 (1975), no. 2, 457–461. MR 385865, DOI 10.2140/pjm.1975.58.457
Sze-tsen Hu, Theory of retracts, Wayne State University Press, Detroit, 1965. MR 0181977
A. Marin and Y. M. Visetti, A general proof of Bing’s shrinkability criterion, Proc. Amer. Math. Soc. 53 (1975), no. 2, 501–507. MR 388319, DOI 10.1090/S0002-9939-1975-0388319-X

Concerning locally homotopy negligible sets and characterization of

manifolds

James E. West, Mapping cylinders of Hilbert cube factors, General Topology and Appl. 1 (1971), no. 2, 111–125. MR 288788, DOI 10.1016/0016-660X(71)90117-6
R. C. Lacher, Cell-like mappings. I, Pacific J. Math. 30 (1969), 717–731. MR 251714, DOI 10.2140/pjm.1969.30.717
T. A. Chapman, Lectures on Hilbert cube manifolds, Regional Conference Series in Mathematics, No. 28, American Mathematical Society, Providence, R.I., 1976. Expository lectures from the CBMS Regional Conference held at Guilford College, October 11-15, 1975. MR 0423357, DOI 10.1090/cbms/028