JournalsjemsVol. 11 , No. 1DOI 10.4171/jems/146

On the topology of positively curved Bazaikin spaces

  • Luis A. Florit

    Instituto de Matemática Pura e Aplicada, Rio de Janeiro, Brazil
  • Wolfgang Ziller

    University of Pennsylvania, Philadelphia, USA
On the topology of positively curved Bazaikin spaces cover

Abstract

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.