English

Rank three geometry and positive curvature

Differential Geometry 2016-07-15 v1 Group Theory Geometric Topology

Abstract

An axiomatic characterization of buildings of type \CC3\CC_3 due to Tits is used to prove that any cohomogeneity two polar action of type \CC3\CC_3 on a positively curved simply connected manifold is equivariantly diffeomorphic to a polar action on a rank one symmetric space. This includes two actions on the Cayley plane whose associated \CC3\CC_3 type geometry is not covered by a building.

Keywords

Cite

@article{arxiv.1607.04134,
  title  = {Rank three geometry and positive curvature},
  author = {Fuquan Fang and Karsten Grove and Gudlaugur Thorbergsson},
  journal= {arXiv preprint arXiv:1607.04134},
  year   = {2016}
}