Cut-and-Paste on Foliated Bundles

推广Penrose剪切-粘贴方法：带压强和能流的零壳

Generalizing the Penrose cut-and-paste method: Null shells with pressure and energy flux

本文推广Penrose剪切-粘贴方法，推导常曲率时空零边界匹配的局部Lipschitz连续度规及对应坐标变换，实现对含任意引力/物质组分的零壳的构造，并给出闵氏空间中带非平凡能密、能流和压强的零壳示例。

广义Luttinger手术及广义复几何中的其他剪切-粘贴构造

Generalized Luttinger surgery and other cut-and-paste constructions in generalized complex geometry

本文利用稳定广义复结构与辛结构的亲和性，将辛几何中的Luttinger手术、Gluck扭转和分支覆盖推广到广义复几何，并在多种高维流形上构造出具有非伦等价类型变化轨迹分支的稳定广义复结构。

Elliptic Operators and Higher Signatures

Building on the theory of elliptic operators, we give a unified treatment of the following topics: - the problem of homotopy invariance of Novikov's higher signatures on closed manifolds; - the problem of cut-and-paste invariance of Novikov's higher signatures on closed manifolds; - the problem of defining higher signatures on manifolds with boundary and proving their homotopy invariance.

Foliations with all non-closed leaves on non-compact surfaces

Let $X$ be a connected non-compact $2$-dimensional manifold possibly with boundary and $Δ$ be a foliation on $X$ such that each leaf $ω\inΔ$ is homeomorphic to $\mathbb{R}$ and has a trivially foliated neighborhood. Such foliations on the plane were studied by W. Kaplan who also gave their topological classification. He proved that the plane splits into a family of open strips foliated by parallel lines and glued along some boundary intervals. However W. Kaplan's construction depends on a choice of those intervals, and a foliation is described in a non-unique way. We propose a canonical cuttin…

叶状流的迹公式

A trace formula for foliated flows

本文针对闭流形上的余维数1叶状流，通过定义Lefschetz分布并利用b-迹等重整化过程，证明了基于闭轨道与保叶无穷小数据的迹公式，从而解决了C.~Deninger关于两个叶向简约上同调的猜想。