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On the homotopy type of Eschenburg spaces with positive sectional curvature
Author(s):
L.
Astey;
E.
Micha;
G.
Pastor
Journal:
Proc. Amer. Math. Soc.
132
(2004),
3725-3729.
MSC (2000):
Primary 53C20, 53C25, 57N65;
Secondary 57R55
Posted:
July 12, 2004
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Abstract:
A rigidity theorem is proved for principal Eschenburg spaces of positive sectional curvature. It is shown that for a very large class of such spaces the homotopy type determines the diffeomorphism type.
References:
-
- 1.
- L. Astey, E. Micha and G. Pastor, Homeomorphism and diffeomorphism types of Eschenburg spaces. Differential Geom. Appl. 7 (1997), 41-50. MR 98h:53072
- 2.
- J. H. Eschenburg, New examples of manifolds with strictly positive curvature. Invent. Math. 66 (1982), 469-480. MR 83i:53061
- 3.
- J. H. Eschenburg, Cohomology of biquotients. Manuscripta Math. 75 (1992), 151-166. MR 93e:57070
- 4.
- J. H. Eschenburg, Inhomogeneous spaces of positive curvature. Differential Geom. Appl. 2 (1992), 123-132. MR 94j:53044
- 5.
- B. Kruggel, A homotopy classification of certain
 manifolds. Trans. Amer. Math. Soc. 349 (1997), 2827-2843. MR 97m:55012 - 6.
- J. Milgram, The classification of Aloff-Wallach manifolds and their generalizations. Surveys on surgery theory, Vol 1. Annals of Math. Studies 145 (2000), 379-407. MR 2000m:57056
- 7.
- I. Niven, H. Zuckerman and H. Montgomery, An introduction to the theory of numbers. 5th edition, John Wiley and Sons, New York, 1991. MR 91i:11001
- 8.
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Additional Information:
L.
Astey
Affiliation:
Departamento de Matemáticas, Centro de Investigación y Estudios Avanzados del IPN, Apartado Postal 14-740, México D.F. 07000
Email:
lastey@math.cinvestav.mx
E.
Micha
Affiliation:
Departamento de Matemáticas, Centro de Investigación y Estudios Avanzados del IPN, Apartado Postal 14-740, México D.F. 07000
Email:
emicha@math.cinvestav.mx
G.
Pastor
Affiliation:
Instituto Tecnológico Autónomo de México (ITAM), Río Hondo No. 1, San Angel, México D.F. 01000
Email:
pastor@itam.mx
DOI:
10.1090/S0002-9939-04-07371-X
PII:
S 0002-9939(04)07371-X
Keywords:
Eschenburg spaces,
homotopy types,
diffeomorphism types
Received by editor(s):
March 17, 2003
Received by editor(s) in revised form:
June 12, 2003.
Posted:
July 12, 2004
Additional Notes:
Research supported by Conacyt grant 28783E and by Asociación Mexicana de Cultura, A.C
Communicated by:
Jon G. Wolfson
Copyright of article:
Copyright
2004,
American Mathematical Society
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