Finding a boundary for a Menger manifold

Chigogidze, A.

doi:10.1090/S0002-9939-1994-1231030-5

Finding a boundary for a Menger manifold
HTML articles powered by AMS MathViewer

by A. Chigogidze PDF

Proc. Amer. Math. Soc. 121 (1994), 631-640 Request permission

Abstract:

We give a characterization of k-dimensional $(k \geq 1)$ Menger manifolds admitting boundaries in the sense of Chapman and Siebenmann.

References

Mladen Bestvina, Characterizing $k$-dimensional universal Menger compacta, Bull. Amer. Math. Soc. (N.S.) 11 (1984), no. 2, 369–370. MR 752801, DOI 10.1090/S0273-0979-1984-15313-8
W. Browder, J. Levine, and G. R. Livesay, Finding a boundary for an open manifold, Amer. J. Math. 87 (1965), 1017–1028. MR 189046, DOI 10.2307/2373259
Morton Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478–483. MR 115157, DOI 10.1090/S0002-9939-1960-0115157-4
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
T. A. Chapman and L. C. Siebenmann, Finding a boundary for a Hilbert cube manifold, Acta Math. 137 (1976), no. 3-4, 171–208. MR 425973, DOI 10.1007/BF02392417
A. Ch. Chigogidze, Compact spaces lying in the $n$-dimensional universal Menger compact space and having homeomorphic complements in it, Mat. Sb. (N.S.) 133(175) (1987), no. 4, 481–496, 559 (Russian); English transl., Math. USSR-Sb. 61 (1988), no. 2, 471–484. MR 911804, DOI 10.1070/SM1988v061n02ABEH003219
A. Ch. Chigogidze, Theory of $n$-shapes, Uspekhi Mat. Nauk 44 (1989), no. 5(269), 117–140 (Russian); English transl., Russian Math. Surveys 44 (1989), no. 5, 145–174. MR 1040271, DOI 10.1070/RM1989v044n05ABEH002279
A. Ch. Chigogidze, $n$-shapes and $n$-cohomotopy groups of compacta, Mat. Sb. 180 (1989), no. 3, 322–335, 432 (Russian); English transl., Math. USSR-Sb. 66 (1990), no. 2, 329–342. MR 993228, DOI 10.1070/SM1990v066n02ABEH001316
A. Chigogidze, Classification theorem for Menger manifolds, Proc. Amer. Math. Soc. 116 (1992), no. 3, 825–832. MR 1143015, DOI 10.1090/S0002-9939-1992-1143015-6
A. Chigogidze, $UV^n$-equivalence and $n$-equivalence, Proceedings of the Tsukuba Topology Symposium (Tsukuba, 1990), 1992, pp. 283–291. MR 1180815, DOI 10.1016/0166-8641(92)90010-W
Ralph H. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. (2) 42 (1941), 333–370. MR 4108, DOI 10.2307/1968905
R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), no. 4, 495–552. MR 645403, DOI 10.1090/S0002-9904-1977-14321-8
Scott C. Metcalf, Finding a boundary for a Hilbert cube manifold bundle, Pacific J. Math. 120 (1985), no. 1, 153–178. MR 808935

The obstruction to finding a boundary for an open manifold of dimension greater than five

C. T. C. Wall, Finiteness conditions for $\textrm {CW}$-complexes, Ann. of Math. (2) 81 (1965), 56–69. MR 171284, DOI 10.2307/1970382
J. H. C. Whitehead, Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55 (1949), 213–245. MR 30759, DOI 10.1090/S0002-9904-1949-09175-9