Finding a boundary for a Menger manifold
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- by A. Chigogidze
- Proc. Amer. Math. Soc. 121 (1994), 631-640
- DOI: https://doi.org/10.1090/S0002-9939-1994-1231030-5
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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.Β 2, 369β370. 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), 1017β1028. MR 189046, DOI 10.2307/2373259
- Morton Brown, Some applications of an approximation theorem for inverse limits, Proc. Amer. Math. Soc. 11 (1960), 478β483. 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.Β 3-4, 171β208. 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.Β 4, 481β496, 559 (Russian); English transl., Math. USSR-Sb. 61 (1988), no.Β 2, 471β484. MR 911804, DOI 10.1070/SM1988v061n02ABEH003219
- A. Ch. Chigogidze, Theory of $n$-shapes, Uspekhi Mat. Nauk 44 (1989), no.Β 5(269), 117β140 (Russian); English transl., Russian Math. Surveys 44 (1989), no.Β 5, 145β174. MR 1040271, DOI 10.1070/RM1989v044n05ABEH002279
- A. Ch. Chigogidze, $n$-shapes and $n$-cohomotopy groups of compacta, Mat. Sb. 180 (1989), no.Β 3, 322β335, 432 (Russian); English transl., Math. USSR-Sb. 66 (1990), no.Β 2, 329β342. MR 993228, DOI 10.1070/SM1990v066n02ABEH001316
- A. Chigogidze, Classification theorem for Menger manifolds, Proc. Amer. Math. Soc. 116 (1992), no.Β 3, 825β832. 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.Β 283β291. MR 1180815, DOI 10.1016/0166-8641(92)90010-W
- Ralph H. Fox, On the Lusternik-Schnirelmann category, Ann. of Math. (2) 42 (1941), 333β370. MR 4108, DOI 10.2307/1968905
- R. C. Lacher, Cell-like mappings and their generalizations, Bull. Amer. Math. Soc. 83 (1977), no.Β 4, 495β552. 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.Β 1, 153β178. MR 808935 L. C. Siebenmann, The obstruction to finding a boundary for an open manifold of dimension greater than five, Doctoral dissertation, Princeton Univ., Princeton, NJ, 1965.
- C. T. C. Wall, Finiteness conditions for $\textrm {CW}$-complexes, Ann. of Math. (2) 81 (1965), 56β69. MR 171284, DOI 10.2307/1970382
- J. H. C. Whitehead, Combinatorial homotopy. I, Bull. Amer. Math. Soc. 55 (1949), 213β245. MR 30759, DOI 10.1090/S0002-9904-1949-09175-9
Bibliographic Information
- © Copyright 1994 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 121 (1994), 631-640
- MSC: Primary 57Q12; Secondary 55P55, 57N99
- DOI: https://doi.org/10.1090/S0002-9939-1994-1231030-5
- MathSciNet review: 1231030