27 citations · 78 across the 12 of their papers we have counts for
7 papers · 1 filter
A Toponogov globalisation result for Lorentzian length spaces
Tobias Beran, John Harvey, Lewis Napper +1
In the synthetic geometric setting introduced by Kunzinger and Sämann, we present an analogue of Toponogov's Globalisation Theorem which applies to Lorentzian length spaces with lo…
Almost non-negatively curved 4-manifolds with torus symmetry
John Harvey, Catherine Searle
We prove that if a closed, smooth, simply-connected 4-manifold with a circle action admits an almost non-negatively curved sequence of invariant Riemannian metrics, then it also ad…
Positively curved Riemannian orbifolds and Alexandrov spaces with circle symmetry in dimension 4
John Harvey, Catherine Searle
We classify positively curved Alexandrov spaces of dimension 4 with an isometric circle action up to equivariant homeomorphism, subject to a certain additional condition on the inf…
Semi-free actions with manifold orbit spaces
John Harvey, Martin Kerin, Krishnan Shankar
In this paper, we study smooth, semi-free actions on closed, smooth, simply connected manifolds, such that the orbit space is a smoothable manifold. We show that the only simply co…
Orbifold finiteness under geometric and spectral constraints
John Harvey
The class of Riemannian orbifolds of dimension n defined by a lower bound on the sectional curvature and the volume and an upper bound on the diameter has only finitely many member…
Equivariant Alexandrov geometry and orbifold finiteness
John Harvey
Let a compact Lie group act isometrically on a non-collapsing sequence of compact Alexandrov spaces with fixed dimension and uniform lower curvature and upper diameter bounds. If t…
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…