Topological finiteness theorems for manifolds in Gromov-Hausdorff space
Steven C. Ferry
Source: Duke Math. J. Volume 74, Number 1
(1994), 95-106.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077288010
Mathematical Reviews number (MathSciNet): MR1271464
Zentralblatt MATH identifier: 0824.53040
Digital Object Identifier: doi:10.1215/S0012-7094-94-07404-8
References
[A] J. F. Adams, Stable homotopy and generalised homology, University of Chicago Press, Chicago, Ill., 1974.
Mathematical Reviews (MathSciNet): MR53:6534
Zentralblatt MATH: 0309.55016
[Au] K. K. Au Thesis, University of California at San Diego, 1990.
[B1] K. Borsuk, On some metrizations of the hyperspace of compact sets, Fund. Math. 41 (1955), 168–202.
Mathematical Reviews (MathSciNet): MR16,946c
Zentralblatt MATH: 0065.38102
[B2] K. Borsuk, Theory of Shape, vol. 59, PWN—Polish Scientific Publishers, Warsaw, 1975.
Mathematical Reviews (MathSciNet): MR54:6132
Zentralblatt MATH: 0317.55006
[Ch] T. A. Chapman, Invariance of torsion and the Borsuk conjecture, Canad. J. Math. 32 (1980), no. 6, 1333–1341.
Mathematical Reviews (MathSciNet): MR82i:57019
Zentralblatt MATH: 0539.57009
[ChF] T. A. Chapman and S. C. Ferry, Approximating homotopy equivalences by homeomorphisms, Amer. J. Math. 101 (1979), no. 3, 583–607.
Mathematical Reviews (MathSciNet): MR81f:57007b
Zentralblatt MATH: 0426.57004
Digital Object Identifier: doi:10.2307/2373799
JSTOR: links.jstor.org
[D] A. N. Dranishnikov, On a problem of P. S. Aleksandrov, Mat. Sb. (N.S.) 135(177) (1988), no. 4, 551–557, 560.
Mathematical Reviews (MathSciNet): MR90e:55004
Zentralblatt MATH: 0643.55001
[DF] A. N. Dranishnikov and S. C. Ferry, Cell-like images of topological manifolds and limits of manifolds in Gromov-Hausdorff space, preprint.
[F1] S. Ferry, A stable converse to the Vietoris-Smale theorem with applications to shape theory, Trans. Amer. Math. Soc. 261 (1980), no. 2, 369–386.
Mathematical Reviews (MathSciNet): MR82c:55018
Zentralblatt MATH: 0452.57002
Digital Object Identifier: doi:10.2307/1998371
[F2] S. Ferry, Counting simple-homotopy types in Gromov-Hausdorff space, preprint.
[FO] S. Ferry and B. L. Okun, Approximating topological metrics by Riemannian metrics, to appear in Proc. Amer. Math. Soc.
Mathematical Reviews (MathSciNet): MR1246524
Zentralblatt MATH: 0828.53038
Digital Object Identifier: doi:10.2307/2161004
JSTOR: links.jstor.org
[FW] S. C. Ferry and S. Weinberger, Curvature, tangentiality, and controlled topology, Invent. Math. 105 (1991), no. 2, 401–414.
Mathematical Reviews (MathSciNet): MR94c:57043
Zentralblatt MATH: 0744.57017
Digital Object Identifier: doi:10.1007/BF01232272
[GrP] R. E. Greene and P. Petersen, Little topology, big volume, Duke Math. J. 67 (1992), no. 2, 273–290.
Mathematical Reviews (MathSciNet): MR93f:53035
Zentralblatt MATH: 0772.53033
Digital Object Identifier: doi:10.1215/S0012-7094-92-06710-X
Project Euclid: euclid.dmj/1077294404
[GLP] M. Gromov, Structures métriques pour les variétés riemanniennes, Textes Mathématiques [Mathematical Texts], vol. 1, CEDIC, Paris, 1981.
Mathematical Reviews (MathSciNet): MR85e:53051
Zentralblatt MATH: 0509.53034
[G] K. Grove, Metric differential geometry, Differential geometry (Lyngby, 1985), Lecture Notes in Math., vol. 1263, Springer, Berlin, 1987, pp. 171–227.
Mathematical Reviews (MathSciNet): MR88i:53075
Zentralblatt MATH: 0622.53022
Digital Object Identifier: doi:10.1007/BFb0078613
[GP] K. Grove and P. Petersen, Bounding homotopy types by geometry, Ann. of Math. (2) 128 (1988), no. 1, 195–206.
Mathematical Reviews (MathSciNet): MR90a:53044
Zentralblatt MATH: 0655.53032
Digital Object Identifier: doi:10.2307/1971439
JSTOR: links.jstor.org
[GPW1] K. Grove, P. Petersen, and J. Wu, Geometric finiteness theorems via controlled topology, Invent. Math. 99 (1990), no. 1, 205–213.
Mathematical Reviews (MathSciNet): MR90k:53075
Zentralblatt MATH: 0747.53033
Digital Object Identifier: doi:10.1007/BF01234417
[GPW2] K. Grove, P. Petersen, and J. Wu, Erratum: “Geometric finiteness theorems via controlled topology”, Invent. Math. 104 (1991), no. 1, 221–222.
Mathematical Reviews (MathSciNet): MR92b:53065
Digital Object Identifier: doi:10.1007/BF01245073
[HM] M. W. Hirsch and B. Mazur, Smoothings of piecewise linear manifolds, Princeton University Press, Princeton, N. J., 1974.
Mathematical Reviews (MathSciNet): MR54:3711
Zentralblatt MATH: 0298.57007
[J] W. Jakobsche, The Bing-Borsuk conjecture is stronger than the Poincaré conjecture, Fund. Math. 106 (1980), no. 2, 127–134.
Mathematical Reviews (MathSciNet): MR81i:57007
Zentralblatt MATH: 0362.54029
[KS] R. C. Kirby and L. C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Princeton University Press, Princeton, N.J., 1977.
Mathematical Reviews (MathSciNet): MR58:31082
Zentralblatt MATH: 0361.57004
[MM] I. Madsen and R. J. Milgram, The classifying spaces for surgery and cobordism of manifolds, Annals of Mathematics Studies, vol. 92, Princeton University Press, Princeton, N.J., 1979.
Mathematical Reviews (MathSciNet): MR81b:57014
Zentralblatt MATH: 0446.57002
[M] T. Engel Moore, Gromov-Hausdorff convergence to non-manifolds, to appear in J. Geom. Anal.
Mathematical Reviews (MathSciNet): MR1360828
Zentralblatt MATH: 0836.57015
[MT] R. E. Mosher and M. C. Tangora, Cohomology operations and applications in homotopy theory, Harper & Row Publishers, New York, 1968.
Mathematical Reviews (MathSciNet): MR37:2223
Zentralblatt MATH: 0153.53302
[N] A. J. Nicas, Induction theorems for groups of homotopy manifold structures, Mem. Amer. Math. Soc. 39 (1982), no. 267, vi+108.
Mathematical Reviews (MathSciNet): MR83i:57026
Zentralblatt MATH: 0507.57018
[P1] P. Petersen, A finiteness theorem for metric spaces, J. Differential Geom. 31 (1990), no. 2, 387–395.
Mathematical Reviews (MathSciNet): MR91d:53070
Zentralblatt MATH: 0696.55005
Project Euclid: euclid.jdg/1214444319
[P2] P. Petersen, Gromov-Hausdorff convergence of metric spaces, to appear in Proc. Sympos. Pure Math.
Mathematical Reviews (MathSciNet): MR1216641
Zentralblatt MATH: 0788.53037
[Q] F. Quinn, Ends of maps. III. Dimensions $4$ and $5$, J. Differential Geom. 17 (1982), no. 3, 503–521.
Mathematical Reviews (MathSciNet): MR84j:57012
Zentralblatt MATH: 0533.57009
Project Euclid: euclid.jdg/1214437139
[Ra] A. Ranicki, The total surgery obstruction, Algebraic topology, Aarhus 1978 (Proc. Sympos., Univ. Aarhus, Aarhus, 1978), Lecture Notes in Math., vol. 763, Springer, Berlin, 1979, pp. 275–316.
Mathematical Reviews (MathSciNet): MR81e:57034
Zentralblatt MATH: 0428.57012
[S] J.-P. Serre, Groupes d'homotopie et classes de groupes abéliens, Ann. of Math. (2) 58 (1953), 258–294.
Mathematical Reviews (MathSciNet): MR15,548c
Zentralblatt MATH: 0052.19303
Digital Object Identifier: doi:10.2307/1969789
JSTOR: links.jstor.org
[Si] L. C. Siebenmann, Topological manifolds, Actes du Congrès International des Mathématiciens (Nice, 1970), Tome 2, Gauthier-Villars, Paris, 1971, pp. 133–163.
Mathematical Reviews (MathSciNet): MR54:11335
Zentralblatt MATH: 0224.57001
[Wa] C. T. C. Wall, Surgery on compact manifolds, Academic Press, London, 1970.
Mathematical Reviews (MathSciNet): MR55:4217
Zentralblatt MATH: 0219.57024
[Walsh] J. J. Walsh, Dimension, cohomological dimension, and cell-like mappings, Shape theory and geometric topology (Dubrovnik, 1981), Lecture Notes in Math., vol. 870, Springer, Berlin, 1981, pp. 105–118.
Mathematical Reviews (MathSciNet): MR83a:57021
Zentralblatt MATH: 0474.55002
Digital Object Identifier: doi:10.1007/BFb0089711
[W] S. Weinberger, The Topological Classification of Stratified Spaces, to appear from Univ. of Chicago Press, Chicago.
Mathematical Reviews (MathSciNet): MR1308714
Zentralblatt MATH: 0826.57001
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