Controlled topology in geometry
Authors:
K. Grove, P. Petersen V and J. Y. Wu
Journal:
Bull. Amer. Math. Soc. 20 (1989), 181183
MSC (1985):
Primary 53C20, 57N99
DOI:
https://doi.org/10.1090/S027309791989157558
MathSciNet review:
974425
Fulltext PDF
References  Similar Articles  Additional Information

[B] E. G. Begle, Regular convergence, Duke Math. J. 11 (1944), 441450. MR 10964

[CF] T. A. Chapman and S. Ferry, Approximating homotopy equivalences by homeomorphisms, Amer. J. Math. 101 (1979), 583607. MR 533192

[C] J. Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 6174. 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 celllike maps, Proc. Internat. Congr. Math. Helsinki 1978 (O. Lehto, ed.), Acad. Sci. Fenn., Helsinki, 1980, pp. 111127. MR 562601

[F] S. Ferry, Homotoping єmaps to homeomorphisms, Amer. J. Math. 101 (1979), 567582. MR 533191

[G] M. Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 183215. MR 623534

[GP] K. Grove and P. Petersen V, Bounding homotopy types by geometry, Ann. of Math. (2) 128 (1988), 195206. MR 951512

[H] R. S. Hamilton, Threemanifolds with positive Ricci curvature, J. Differential Geom. 17 (1982), 255306. MR 664497

[HK] I. Hambleton and M. Kreck, On the classification of topological 4manifolds with finite fundamental group, Math. Ann. 280 (1988), 85104. 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), 7782. 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), 285291. MR 894878

[Y] T. Yamaguchi, Homotopy finiteness theorems for certain precompact families of Riemannian manifolds, Proc. Amer. Math. Soc. 102 (1988), 660666. MR 928999
Retrieve articles in Bulletin of the American Mathematical Society with MSC (1985): 53C20, 57N99
Retrieve articles in all journals with MSC (1985): 53C20, 57N99
Additional Information
DOI:
https://doi.org/10.1090/S027309791989157558