Promoting Essential Laminations

Sutured manifold hierarchies, essential laminations, and Dehn surgery

We use sutured manifold theory, essential laminations and essential branched surfaces to establish the upper bounds of distances between certain types of nonsimple Dehn surgery slopes. This is the revised version of an earlier preprint {\it Dehn surgery and simple manifolds.}

Finite height lamination spaces for surfaces

We describe spaces of essential finite height (measured) laminations in a surface $S$ using a parameter space we call $\mathbb S$, an ordered semi-ring. We show that for every finite height essential lamination $L$ in $S$, there is an action of $π_1(S)$ on an $\mathbb S$-tree dual to the lift of $L$ to the universal cover of $S$.

Measured lamination spaces for surface pairs

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."

Persistent laminations from Seifert surfaces

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 present a method for building persistent laminations for knots from an incompressible Seifert surface for some `parent' knot. Using this construction, we can, for example, currently build persistent laminations for approximately 45 percent of the knots in the standard knot tables; …

Laminations and groups of homeomorphisms of the circle

If M is an atoroidal 3-manifold with a taut foliation, Thurston showed that pi_1(M) acts on a circle. Here, we show that some other classes of essential laminations also give rise to actions on circles. In particular, we show this for tight essential laminations with solid torus guts. We also show that pseudo-Anosov flows induce actions on circles. In all cases, these actions can be made into faithful ones, so pi_1(M) is isomorphic to a subgroup of Homeo(S^1). In addition, we show that the fundamental group of the Weeks manifold has no faithful action on S^1. As a corollary, the Weeks manifold…

通过实测层叠（Measured Laminations）计算本质曲面的增长率

Growth Rate of Essential Surfaces via Measured Laminations

该研究在哈肯3-流形中建立了$\text{ML}$及$\text{ML}_0$维数与正规曲面的关联，进而推导了特定双曲3-流形中高欧拉特征闭定向本质曲面数量的渐近增长规律。