27 citations · 68 across the 17 of their papers we have counts for
5 papers · 2 filters
Orientation and symmetries of Alexandrov spaces with applications in positive curvature
John Harvey, Catherine Searle
We develop two new tools for use in Alexandrov geometry: a theory of ramified orientable double covers and a particularly useful version of the Slice Theorem for actions of compact…
Positively curved manifolds with maximal symmetry rank
Karsten Grove, Catherine Searle
The symmetry-rank of a riemannian manifold is by definition the rank of its isometry group. We determine precisely which smooth closed manifolds admit a positively curved metric wi…
Low-dimensional manifolds with non-negative curvature and maximal symmetry rank
Fernando Galaz-Garcia, Catherine Searle
We classify closed, simply connected -manifolds of non-negative sectional curvature admitting an isometric torus action of maximal symmetry rank in dimensions . I…
Global G-Manifold reductions and resolutions
Karsten Grove, Catherine Searle
The purpose of this note is to exhibit some simple and basic constructions for smooth compact transformation groups, and some of their most immediate applications to geometry.
The Hopf conjecture for manifolds with low cohomogeneity or high symmetry rank
Thomas Puettmann, Catherine Searle
We prove that the Euler characteristic of an even-dimensional compact manifold with positive (nonnegative) sectional curvature is positive (nonnegative) provided that the manifold…