A Coincidence Formula for Foliated Manifolds

积分叶状单纯体积与遍历分解

Integral foliated simplicial volume and ergodic decomposition

本文建立了积分叶状单纯体积沿遍历分解的积分公式，类比于群的代价的遍历分解公式，为几何拓扑与动力系统交叉领域提供了新工具。

Foliated group actions and cyclic cohomology

We prove a cyclic Lefschetz formula for foliations. To this end, we define a notion of equivariant cyclic cohomology and show that its expected pairing with K-theory is well defined. This enables to associate to any invariant transverse current on a compact foliated manifold, a Lefschetz formula for leafwise preserving isometries.

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。

非正曲率几何中的Borel作用与Nielsen实现问题

Borel actions in nonpositively curved geometry and the Nielsen realisation problem

本文证明了非正曲率流形上等距作用真不动点与同伦不动点重合的定理，并统一了Nielsen实现问题的多种表述。

Analogies between group actions on 3-manifolds and number fields

Mazur, Kapranov, Reznikov, and others developed ``Arithmetic Topology,'' a theory describing some surprising analogies between 3-dimensional topology and number theory, which can be summarized by saying that knots are like prime numbers. We extend their work by proving several formulas concerning branched coverings of 3-manifolds and extensions of number fields and observe that these formulas are almost identical, via the dictionary of arithmetic topology. Until now there is no satisfactory explanation for the coincidences between our formulas. The proofs of topological results use equivariant…