On the topology of positively curved Bazaikin spaces

Florit, Luis A., and Ziller, Wolfgang. "On the topology of positively curved Bazaikin spaces." Journal of the European Mathematical Society 011.1 (2009): 189-205. <http://eudml.org/doc/277425>.

@article{Florit2009,
abstract = {We explore some aspects of the topology of the family of 13-dimensional Bazaikin spaces. Using the computation of their homology rings, Pontryagin classes and linking forms, we show that there is only one Bazaikin space that is homotopy equivalent to a homogeneous space, i.e., the Berger space. Moreover, it is easily shown that there are only finitely many Bazaikin spaces in each homeomorphism type and that there are only finitely many positively curved ones for a given cohomology ring. In fact, supported by computational experiments, it is conjectured that all positively curved Bazaikin spaces are homeomorphically, or at least diffeomorphically, distinct.},
author = {Florit, Luis A., Ziller, Wolfgang},
journal = {Journal of the European Mathematical Society},
keywords = {positive curvature; Bazaikin spaces; positive curvature; Bazaikin spaces; Berger space},
language = {eng},
number = {1},
pages = {189-205},
publisher = {European Mathematical Society Publishing House},
title = {On the topology of positively curved Bazaikin spaces},
url = {http://eudml.org/doc/277425},
volume = {011},
year = {2009},
}

TY - JOUR
AU - Florit, Luis A.
AU - Ziller, Wolfgang
TI - On the topology of positively curved Bazaikin spaces
JO - Journal of the European Mathematical Society
PY - 2009
PB - European Mathematical Society Publishing House
VL - 011
IS - 1
SP - 189
EP - 205
AB - We explore some aspects of the topology of the family of 13-dimensional Bazaikin spaces. Using the computation of their homology rings, Pontryagin classes and linking forms, we show that there is only one Bazaikin space that is homotopy equivalent to a homogeneous space, i.e., the Berger space. Moreover, it is easily shown that there are only finitely many Bazaikin spaces in each homeomorphism type and that there are only finitely many positively curved ones for a given cohomology ring. In fact, supported by computational experiments, it is conjectured that all positively curved Bazaikin spaces are homeomorphically, or at least diffeomorphically, distinct.
LA - eng
KW - positive curvature; Bazaikin spaces; positive curvature; Bazaikin spaces; Berger space
UR - http://eudml.org/doc/277425
ER -