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Controlled topology in geometry
Author(s):
K.
Grove;
P.
Petersen V;
J. Y.
Wu
Journal:
Bull. Amer. Math. Soc.
20
(1989),
181-183.
MSC (1985):
Primary 53C20, 57N99
MathSciNet review:
974425
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References |
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Additional information
References:
- [B] E. G. Begle, Regular convergence, Duke Math. J. 11 (1944), 441-450. MR 10964
- [CF] T. A. Chapman and S. Ferry, Approximating homotopy equivalences by homeomorphisms, Amer. J. Math. 101 (1979), 583-607. MR 533192
- [C] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61-74. MR 263092
- [D] R. J. Daverman, Decompositions of manifolds, Academic Press, New York, 1986. MR 872468
- [E] R. D. Edwards, The topology of manifolds and cell-like maps, Proc. Internat. Congr. Math. Helsinki 1978 (O. Lehto, ed.), Acad. Sci. Fenn., Helsinki, 1980, pp. 111-127. MR 562601
- [F] S. Ferry, Homotoping є-maps to homeomorphisms, Amer. J. Math. 101 (1979), 567-582. MR 533191
- [G] M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 183-215. MR 623534
- [GP] K. Grove and P. Petersen V, Bounding homotopy types by geometry, Ann. of Math. (2) 128 (1988), 195-206. MR 951512
- [H] R. S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255-306. MR 664497
- [HK] I. Hambleton and M. Kreck, On the classification of topological 4-manifolds with finite fundamental group, Math. Ann. 280 (1988), 85-104. MR 928299
- [KS] R. Kirby and L. Siebenmann, Foundational essays on topological manifolds, smoothings and triangulations, Ann. of Math. Studies 88, Princeton Univ. Press, Princeton, N. J., 1977. MR 645390
- [P] S. Peters, Cheeger's finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 394 (1984), 77-82. MR 743966
- [PV] P. Petersen V, A finiteness theorem for metric spaces, J. Differential Geom. (to appear). MR 1037407
- [Q] F. Quinn, An obstruction to the resolution of homology manifolds, Michigan Math. J. 34 (1987), 285-291. MR 894878
- [Y] T. Yamaguchi, Homotopy finiteness theorems for certain precompact families of Riemannian manifolds, Proc. Amer. Math. Soc. 102 (1988), 660-666. MR 928999
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Additional Information:
DOI:
10.1090/S0273-0979-1989-15755-8
PII:
S 0273-0979(1989)15755-8
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