In this note we study the topology of the positively curved Bazaikin spaces. We show that the only Bazaikin space that is homotopically equivalent to a homogeneous space is the Berger space. Moreover, we compute their Pontryagin classes and linking form to conclude that there is no pair of positively curved Bazaikin spaces which are homeomorphic, at least if the order of the sixth cohomology group with integer coefficients is less than 108.
Cite this article
Luis A. Florit, Wolfgang Ziller, On the topology of positively curved Bazaikin spaces. J. Eur. Math. Soc. 11 (2009), no. 1, pp. 189–205DOI 10.4171/JEMS/146