Complex twist flows on surface group representations and the local shape of the deformation space of hyperbolic cone-3-manifolds

Abstract

In two former papers, the authors independently proved that the space of hyperbolic cone-3-manifolds with cone angles less than 2π and fixed singular locus is locally parametrized by the cone angles. In this sequel, we investigate the local shape of the deformation space when the singular locus is no longer fixed, i.e. when the singular vertices can be split. We show that the different possible splittings correspond to specific pair-of-pants decompositions of the smooth parts of the links of the singular vertices, and that under suitable assumptions the corresponding subspace of deformations is parametrized by the cone angles of the original edges and the lengths of the new ones.

43 pages, 7 figures, title changed, overall organization of the paper modified, some corrections, new material added

References in corpus (5)

• Minimal surfaces and particles in 3-manifolds
• Deforming Euclidean cone 3-manifolds
• The complex-symplectic geometry of SL(2,C)-characters over surfaces
• Regenerating hyperbolic cone structures from Nil
• The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than $2\pi$

Cited by in corpus (1)

• The deformation theory of hyperbolic cone-3-manifolds with cone-angles less than $2\pi$