Deforming Euclidean cone 3-manifolds

Abstract

Given a closed orientable Euclidean cone 3-manifold C with cone angles less than or equal to pi, and which is not almost product, we describe the space of constant curvature cone structures on C with cone angles less than pi. We establish a regeneration result for such Euclidean cone manifolds into spherical or hyperbolic ones and we also deduce global rigidity for Euclidean cone structures.

Only changes for the grants footnotes have been made

Cited by in corpus (14)

• Geometric transition from hyperbolic to anti-de Sitter structures in dimension four
• The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than $2\pi$
• Explicit formulae for Chern-Simons invariants of the hyperbolic orbifolds of the knot with Conway's notation $C(2n,3)$
• Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone-3-manifolds
• The A-polynomial 2-tuple of twisted Whitehead links
• Character varieties of a transitioning Coxeter 4-orbifold
• On the volume of double twist link cone-manifolds
• Volumes of double twist knot cone-manifolds
• The volume of hyperbolic cone-manifolds of the knot with Conway's notation $C(2n,3)$
• Singular vertices of nonnegatively curved integral polyhedral 3-manifolds
• Examples of character varieties in characteristic $p$ and ramification
• Trigonometric identities and volumes of the hyperbolic twist knot cone-manifolds
• Explicit formulae for Chern-Simons invariants of the hyperbolic $J(2n,-2m)$ knot orbifolds
• On the volume and the Chern-Simons invariant for the hyperbolic alternating knot orbifolds