30 research outputs found
Homoclinic leaves, Hausdorff limits and homeomorphisms
We show that except for one exceptional case, a lamination on the boundary of
a 3-dimensional handlebody H is a Hausdorff limit of meridians if and only if
it is commensurable to a lamination with a 'homoclinic leaf'. This is a precise
version of a philosophy called Casson's Criterion, which appeared in
unpublished notes of A. Casson. Applications include a characterization of when
a non-minimal lamination is a Hausdorff limit of meridians, in terms of
properties of its minimal components, and a related characterization of which
reducible self-homeomorphisms of the boundary of H have powers that extend to
subcompressionbodies of H.Comment: 74 page
Convexity of strata in diagonal pants graphs of surfaces
We prove a number of convexity results for strata of the diagonal pants graph
of a surface, in analogy with the extrinsic geometric properties of strata in
the Weil-Petersson completion. As a consequence, we exhibit convex flat
subgraphs of every possible rank inside the diagonal pants graph.Comment: 14 pages, 4 figure
Mixing invariants of hyperbolic 3-manifolds
Let M be a compact hyperbolic 3-manifold with incompressible boundary. Consider a complete hyperbolic metric on int(M). To each geometrically finite end of int(M) are traditionnaly associated 3 different invariants : the hyperbolic metric associated to the conformal structure at infinity, the hyperbolic metric on the boundary of the convex core and the bending measured lamination of the convex core. In this note we show how invariants of different types can be realised in the different ends
Mixing invariants of hyperbolic 3-manifolds
Let M be a compact hyperbolic 3-manifold with incompressible boundary. Consider a complete hyperbolic metric on int(M). To each geometrically finite end of int(M) are traditionnaly associated 3 different
invariants : the hyperbolic metric associated to the conformal structure at
infinity, the hyperbolic metric on the boundary of the convex core and the
bending measured lamination of the convex core. In this note we show how invariants of different types can be realised in the different ends
Continuity of the bending map
17 pages, 2 figures.International audienceThe bending map of a hyperbolic 3-manifold maps a convex cocompact hyperbolic metric on a hyperbolic 3-manifold with boundary to its bending measured geodesic lamination. In the present paper we study the extension of this map to the space of geometrically finite hyperbolic metrics. We introduce a relationship on the space of measured geodesic laminations and shows that the quotient map obtained from the bending map is continuous
An extension of the Masur domain
International audienceThe Masur domain is a subset of the space of projective measured geodesic laminations on the boundary of a 3-manifold M. This domain plays an important role in the study of the hyperbolic structures on the interior of M. In this paper, we define an extension of the Masur domain and explain that it shares a lot of properties with the Masur domain