arXiv research

Defines new lamination links in 3-manifolds and shows their properties.

Extends Seifert's algorithm to lamination links.

Maps and measures on surfaces link best Lipschitz and least gradient functions.

New LP structures for punctured and unpunctured surfaces are discovered.

Paper constructs geometric transitions between hyperbolic and Anti-de Sitter geometries.

In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a flat structure, similar to geodesic laminations on hyperbolic surfaces. Here is a sequel to this article that aims at defining transversal measures on flat laminations similar to transversal measures on hyperbolic laminations, taking i…

Since their introduction by Thurston, measured geodesic laminations on hyperbolic surfaces occur in many contexts. In [Mor], we have introduced a notion of flat laminations on surfaces endowed with a half-translation structure (that is a singular flat surface with holonomy {+/-Id}, similar to geodesic laminations on hy…

Characterizes geodesic laminations on surfaces.

Proves a function's locally least gradient property if its level sets are minimal laminations.

We show that every topological surface lamination of a 3-manifold M is isotopic to one with smoothly immersed leaves. This carries out a project proposed by Gabai in [Problems in foliations and laminations, AMS/IP Stud. Adv. Math. 2.2 1--33]. Consequently any such lamination admits the structure of a Riemann surface la…

A contamination in a 3-manifold is an object interpolating between the contact structure and the lamination. Contaminations seem to provide a link between 3-dimensional contact geometry and the classical topology of 3-manifolds, as described in a separate paper. In this paper we deal with contaminations carried by bran…

We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are indeed the "straightening" of the coarse laminations defined in [Ca], by using minimal surface techniques. Moreover, whe…

New bounds link Schwarzian derivative to hyperbolic geometry.

Generalizes existence of bending laminations for Kleinian groups.

The aim of the paper is to investigate the relation between inverse limit of branched manifolds and codimension zero laminations. We give necessary and sufficient conditions for such an inverse limit to be a lamination. We also show that codimension zero laminations are inverse limits of branched manifolds. The inverse…

Path-connectivity of thick laminations on high-genus surfaces.

Proves rigidity of homeomorphisms for lamination spaces.

We describe a construction of ordered algebraic structures (ordered abelian semigroups, ordered commutative semirings, etc.) and describe applications to codimension-1 laminations. For a suitable ordered semi- algebraic structure $\mathbb L$ and measurable space $X$ we define $\mathbb L$-measures $ν$ on $X$. If $L$ is …

The paper stratifies projective measured laminations and identifies a group of transformations.

Study topological constraints for minimal hyperbolic surface laminations.

A persistent lamination for a knot K is an essential lamination in the complement of K, which remains essential after every non-trivial Dehn surgery along K. Having a persistent lamination implies, for example, that every manifold obtained by non-trivial Dehn surgery along K has universal cover R^3. In this paper we pr…

Let $(M,g,\si)$ be a compact spin manifold of dimension $n \geq 2$. Let $λ_1^+(\tilde{g})$ be the smallest positive eigenvalue of the Dirac operator in the metric $\tilde{g} \in [g]$ conformal to $g$. We then define $\lamin(M,[g],\si) = \inf_{\tilde{g} \in [g]} λ_1^+(\tilde{g}) \Vol(M,\tilde{g})^{1/n} $. We show that $…

Study counts ergodic measures in surface lamination strata.

We calculate a projective space of essential measured laminations in a surface pair, which will be used in another paper to help describe spaces of "finite height laminations."

We examine the dependence of the deformation obtained by bending quasi-Fuchsian structures on the bending lamination. We show that when we consider bending quasi-Fuchsian structures on a closed surface, the conditions obtained by Epstein and Marden to relate weak convergence of arbitrary laminations to the convergence …

We give a Thurston-like definition for laminations on higher Teichmuller spaces associated to a surface $S$ and a semi-simple group $G$ for $G-SL_m$ and $PGL_m$. The case $G=SL_2$ or $PGL_2$ corresponds to the classical theory of laminations. Our construction involves positive configurations of points in the affine bui…

Automorphisms of free groups yield invariant posets of lamination orbits.

Study stretch laminations in hyperbolic 3-manifolds via circle-valued maps.

We investigate the distribution of lengths obtained by intersecting a random geodesic with a geodesic lamination. We give an explicit formula for the distribution for the case of a maximal lamination and show that the distribution is independent of the surface and lamination. We also show how the moments of the distrib…

We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions. In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the exist…

The study characterizes train tracks and measured laminations on infinite surfaces.

Study invariant measures on measured laminations for subgroups of mapping class group.

New proof for solenoidal laminations with symmetric leaves in dimensions other than 4.

New distance function proves rigidity in geodesic lamination space.

Study of laminations for pseudo-Anosov flows on three-manifolds.

Generalizes Candel's theorem on curvature of laminated surfaces.

The paper proves the existence of non-trivial lamination in complex projective space.

Unique hyperbolic manifolds identified by boundary pleating.

Since their introduction by Thurston, geodesic laminations on hyperbolic surfaces occur in many contexts. In this paper, we propose a generalization of geodesic laminations on locally CAT(0), complete, geodesic metric spaces, whose boundary at infinity of the universal cover is endowed with a invariant total cyclic ord…

Characterizes lamination spaces of graphs on a pair of pants.

The paper studies $p$-harmonic functions and their conjugates, showing they converge to calibrations of laminations.

A measured laminations on the universal hyperbolic solenoid $§$ is, by our definition, a leafwise measured lamination with appropriate continuity for the transverse variations. An earthquakes on theuniversal hyperbolic solenoid $§$ is uniquely determined by a measured lamination on $§$; it is a leafwise earthquake with…

Yair Minsky showed that punctured torus groups are classified by a pair of ending laminations (ν_-,ν_+). In this note, we show that there are ending laminations ν_+ such that for any choice of ν_-, the punctured torus group is transcendental as a subgroup of PSL_2 C.

Geometric model of unbounded sl3 laminations with tropical coordinates.

The fundamental germ is a generalization of $π_{1}$, first defined for laminations which arise through group actions in math.DG/0506270. In this paper, the fundamental germ is extended to any lamination having a dense leaf admitting a smooth structure. In addition, an amplification of the fundamental germ called the mo…

Study transverse measures on infinite type hyperbolic surfaces.

Geometrically interprets and computes intersection pairings for higher laminations.

We explicate a number of notions of algebraic laminations existing in the literature, particularly in the context of an exact sequence $1\to H\to G \to Q \to 1$ of hyperbolic groups. These laminations arise in different contexts: existence of Cannon-Thurston maps; closed geodesics exiting ends of manifolds; dual to …