On the topology of positively curved Bazaikin spaces

Details On the topology of positively curved Bazaikin spaces On the topology of positively curved Bazaikin spaces

2006-04-12

arxiv.org/abs/math/0604276v2

Mathematics

Differential Geometry

15 pages

Scientific paper

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.

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