Topological properties of Eschenburg spaces and 3-Sasakian manifolds

Details Topological properties of Eschenburg spaces and 3-Sasakian manifolds Topological properties of Eschenburg spaces and 3-Sasakian manifolds

2004-12-18

arxiv.org/abs/math/0412370v1

Mathematics

Differential Geometry

17 pages

Scientific paper

The authors examine topological properties of the 7-dimensional Eschenburg biquotients diag(z^k1,z^k2,z^k3)\SU(3)/diag(z^l1,z^l2,z^l3). A subfamily of these spaces carry a 3-Sasakian metric. The authors show that among this subfamily there exist many 3-Sasakian spaces which are homeomorphic but not diffeomorphic. In addition, they construct a pair of 3-Sasakian spaces which are diffeomorphic, thus giving the first example of a manifold which carries two non-isometric 3-Sasakian metrics. This answers an open question of C. Boyer and K.Galicki. Among the general family, the authors construct many pairs of positively curved Eschenburg spaces which are homeomorphic but not diffeomorphic. Such pairs were first constructed by Kreck-Stolz among the special subfamily of Aloff-Wallach spaces.

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