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Curvature and finite domination
Author(s):
Michael
Weiss
Journal:
Proc. Amer. Math. Soc.
124
(1996),
615-622.
MSC (1991):
Primary 53C21, 53C20;
Secondary 57Q10
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Abstract:
Upper bounds obtained by Gromov on the Betti numbers of certain closed Riemannian manifolds are shown to be upper bounds on the minimum number of cells in  --spaces dominating such manifolds.
References:
- Abr1
- U. Abresch, Lower curvature bounds, Toponogov's theorem, and bounded topology, Ann. Sci. École Norm. Sup. (4) 18 (1985), 651--670, MR 87j:53058.
- Abr2
- ------, Lower curvature bounds, Toponogov's theorem, and bounded topology, II, Ann. Sci. École Norm. Sup. (4) 20 (1987), 475--502, MR 89d:53080.
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- S. Aloff and N. L. Wallach, An infinite family of distinct 7-manifolds admitting positively curved Riemannian structures, Bull. Amer. Math. Soc. 81 (1975), 93--97, MR 51:6851.
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- A. K. Bousfield and D. M. Kan, Homotopy limits, completions, and localizations, Lecture Notes in Math., vol. 304, Springer-Verlag, New York-Berlin, 1972, MR 51:1825.
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- M.Gromov, Curvature, diameter and Betti numbers, Comment. Math. Helv. 56 (1981), 179--195, MR 82k:53062.
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- ------, Almost flat manifolds, J. Diff. Geom. 13 (1978), 231--243, MR 80h:53041.
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- A. Grothendieck, Sur quelques points d'algèbre homologique, Tôhoku Math. J. (2) 9 (1957), 119--221, MR 21:1328.
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- G. Segal, Classifying spaces and spectral sequences, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 105--112,
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Additional Information:
Michael
Weiss
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109-1003
Address at time of publication:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email:
msweiss@math.lsa.umich.edu
DOI:
10.1090/S0002-9939-96-03056-0
PII:
S 0002-9939(96)03056-0
Keywords:
Positive curvature,
Betti numbers,
homotopy direct limits
Received by editor(s):
February 1, 1994
Received by editor(s) in revised form:
February 22, 1994 and August 9, 1994
Communicated by:
Christopher Croke
Copyright of article:
Copyright
1996,
American Mathematical Society
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