50 research outputs found
On Lorentz spacetimes of constant curvature
We describe in parallel the Lorentzian homogeneous spaces
and ,
and review some recent results relating the geometry of their quotients by
discrete groups.Comment: 16 pages, 2 figures. Appeared in the Proceedings of the December 2012
conference "Groups, Geometry, Dynamics" (Almora, India). Editors: C.S.
Aravinda, W.M. Goldman, K. Gongopadhyay, A. Lubotzky, Mahan Mj, A. Weave
Lengthening deformations of singular hyperbolic tori
Let be a torus with a hyperbolic metric admitting one puncture or cone
singularity. We describe which infinitesimal deformations of lengthen (or
shrink) all closed geodesics. We also study how the answer degenerates when
becomes Euclidean, i.e. very small.Comment: 17 pages, 5 figures. To appear in: Annales de la facult\'e des
sciences de Toulouse (volume dedicated to Michel Boileau's sixtieth birthday
Angled decompositions of arborescent link complements
This paper describes a way to subdivide a 3-manifold into angled blocks,
namely polyhedral pieces that need not be simply connected. When the individual
blocks carry dihedral angles that fit together in a consistent fashion, we
prove that a manifold constructed from these blocks must be hyperbolic. The
main application is a new proof of a classical, unpublished theorem of Bonahon
and Siebenmann: that all arborescent links, except for three simple families of
exceptions, have hyperbolic complements.Comment: 42 pages, 23 figures. Slightly expanded exposition and reference
Convex cocompact actions in real projective geometry
We study a notion of convex cocompactness for (not necessarily irreducible)
discrete subgroups of the projective general linear group acting on real
projective space, and give various characterizations. A convex cocompact group
in this sense need not be word hyperbolic, but we show that it still has some
of the good properties of classical convex cocompact subgroups in rank-one Lie
groups. Extending our earlier work arXiv:1701.09136 from the context of
projective orthogonal groups, we show that for word hyperbolic groups
preserving a properly convex open set in projective space, the above general
notion of convex cocompactness is equivalent to a stronger convex cocompactness
condition studied by Crampon-Marquis, and also to the condition that the
natural inclusion be a projective Anosov representation. We investigate
examples.Comment: 77 pages, 6 figures. Added appendix. Removed section on Anosov
right-angled reflection groups, which will appear as a separate pape