# On the topology of positively curved Bazaikin spaces

Luis A. Florit; Wolfgang Ziller

Journal of the European Mathematical Society (2009)

- Volume: 011, Issue: 1, page 189-205
- ISSN: 1435-9855

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topFlorit, 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 -

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