On the topology of positively curved Bazaikin spaces

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We study the topology of the 13 dimensional positively curved Bazaikin spaces. We show that there is only one such manifold which is homotopy equivalent to a homogeneous space, the so called Berger space. This is in contrast to the case of the 7 dimensional positively curved Eschenburg spaces. In addition, we compute the Pontryagin classes and the linking form and show that the first two billion positively curved Bazaikin manifolds are homeomorphically distinct, raising the question whether this is true in general.
15 pages

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Differential Geometry, Algebraic Topology, 53C20 (primary); 57N65; 57R20 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/111542

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604276
 http://arxiv.org/abs/math/0604276

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arXiv