Controlled topology in geometry
HTML articles powered by AMS MathViewer
- by K. Grove, P. Petersen V and J. Y. Wu PDF
- Bull. Amer. Math. Soc. 20 (1989), 181-183
References
- Edward G. Begle, Regular convergence, Duke Math. J. 11 (1944), 441–450. MR 10964
- Steve Ferry, Homotoping $\varepsilon$-maps to homeomorphisms, Amer. J. Math. 101 (1979), no. 3, 567–582. MR 533191, DOI 10.2307/2373798
- Jeff Cheeger, Finiteness theorems for Riemannian manifolds, Amer. J. Math. 92 (1970), 61–74. MR 263092, DOI 10.2307/2373498
- Robert J. Daverman, Decompositions of manifolds, Pure and Applied Mathematics, vol. 124, Academic Press, Inc., Orlando, FL, 1986. MR 872468
- Robert D. Edwards, The topology of manifolds and cell-like maps, Proceedings of the International Congress of Mathematicians (Helsinki, 1978) Acad. Sci. Fennica, Helsinki, 1980, pp. 111–127. MR 562601
- Steve Ferry, Homotoping $\varepsilon$-maps to homeomorphisms, Amer. J. Math. 101 (1979), no. 3, 567–582. MR 533191, DOI 10.2307/2373798
- Mikhael Gromov, Groups of polynomial growth and expanding maps, Inst. Hautes Études Sci. Publ. Math. 53 (1981), 53–73. MR 623534, DOI 10.1007/BF02698687
- Karsten Grove and Peter Petersen V, Bounding homotopy types by geometry, Ann. of Math. (2) 128 (1988), no. 1, 195–206. MR 951512, DOI 10.2307/1971439
- Richard S. Hamilton, Three-manifolds with positive Ricci curvature, J. Differential Geometry 17 (1982), no. 2, 255–306. MR 664497
- Ian Hambleton and Matthias Kreck, On the classification of topological $4$-manifolds with finite fundamental group, Math. Ann. 280 (1988), no. 1, 85–104. MR 928299, DOI 10.1007/BF01474183
- Robion C. Kirby and Laurence C. Siebenmann, Foundational essays on topological manifolds, smoothings, and triangulations, Annals of Mathematics Studies, No. 88, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1977. With notes by John Milnor and Michael Atiyah. MR 0645390, DOI 10.1515/9781400881505
- Stefan Peters, Cheeger’s finiteness theorem for diffeomorphism classes of Riemannian manifolds, J. Reine Angew. Math. 349 (1984), 77–82. MR 743966, DOI 10.1515/crll.1984.349.77
- Peter Petersen V, A finiteness theorem for metric spaces, J. Differential Geom. 31 (1990), no. 2, 387–395. MR 1037407
- Frank Quinn, An obstruction to the resolution of homology manifolds, Michigan Math. J. 34 (1987), no. 2, 285–291. MR 894878, DOI 10.1307/mmj/1029003559
- Takao Yamaguchi, Homotopy type finiteness theorems for certain precompact families of Riemannian manifolds, Proc. Amer. Math. Soc. 102 (1988), no. 3, 660–666. MR 928999, DOI 10.1090/S0002-9939-1988-0928999-X
Additional Information
- Journal: Bull. Amer. Math. Soc. 20 (1989), 181-183
- MSC (1985): Primary 53C20, 57N99
- DOI: https://doi.org/10.1090/S0273-0979-1989-15755-8
- MathSciNet review: 974425