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Homeomorphism and diffeomorphism types of Eschenburg spaces

✍ Scribed by L Astey; E Micha; G Pastor

Book ID
104358283
Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
674 KB
Volume
7
Category
Article
ISSN
0926-2245

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✦ Synopsis

The machinery of M. Kreck and S. Stoltz is used to obtain a homeomorphism and diffeomorphism classification of a family of Eschenburg spaces. In contrast with the family of Wallach spaces studied by Kreck and Stolz we obtain abundant examples of homeomorphic but not diffeomorphic Eschenburg spaces. Tht problem of stable parallelizability of Eschenburg spaces is discussed in an appendix.

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A space X is called a t-image of Y if C,(X) is homeomorphic to a subspace of C,(Y). We prove that if Y is a t-image of X, then Y is a countable union of images of X under almost lower semicontinuous finite-valued mappings (see Definition 1.4). It follows that if Y is a t-image of X (in particular, i