Useful branched surfaces which carry nothing

A sufficient condition for a branched surface to fully carry a lamination

We give a sufficient condition for a branched surface in a 3 dimensional manifold to fully carry a lamination, giving a piece of answer to a classical question of D. Gabai.

A contamination carrying criterion for branched surfaces

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 branched surfaces, giving a sufficient condition for a branched surface to carry a pure contamination.

端期映射、分裂序列与分支表面

Endperiodic maps, splitting sequences, and branched surfaces

本文通过证明端期映射具有周期性分裂序列，加强了Gabai和Mosher的定理，展示了veering分支表面在缝合 manifold 中的应用及理论扩展。

Branched covers of the sphere and the prime-degree conjecture

To a branched cover between closed, connected and orientable surfaces one associates a "branch datum", which consists of the two surfaces, the total degree d, and the partitions of d given by the collections of local degrees over the branching points. This datum must satisfy the Riemann-Hurwitz formula. A "candidate surface cover" is an abstract branch datum, a priori not coming from a branched cover, but satisfying the Riemann-Hurwitz formula. The old Hurwitz problem asks which candidate surface covers are realizable by branched covers. It is now known that all candidate covers are realizable…

叶状结构欧拉类的一个公式

A formula for the Euler class of foliations

本文通过分支表面的对偶图定义了一个simplicial 1-环，用于表示叶状结构欧拉类的庞加莱对偶，同时推广了Lackenby和Dunfield之前的结论，并观察到某些分支表面满足组合横截面定理。

Anosov flows on Dehn surgeries on the figure-eight knot

The purpose of this paper is to classify Anosov flows on the 3-manifolds obtained by Dehn surgeries on the figure-eight knot. This set of 3-manifolds is denoted by M(r) (r is a ratioanl number), which contains the first class of hyperbolic 3-manifolds admitting Anosov flows in history, discovered by Goodman. Combining with the classification of Anosov flows on the sol-manifold M(0) due to Plante, we have: 1. if r is an integer, up to topological equivalence, M(r) exactly carries a unique Anosov flow, which is constructed by Goodman by doing a Dehn-Fried-Goodman surgery on a suspension Anosov f…