Compact group actions that raise dimension to infinity

A compact group action which raises dimension to infinity

I give a construction of compact group action on a finite dimensional space Y, whose orbit space is infinite dimensional.

无穷远处的链接与非紧致流形上的标量曲率衰减

Linking at Infinity and Scalar Curvature Decay on Non-Compact Manifolds

研究非紧致正标量曲率流形上曲率衰减与无穷远处拓扑结构的关系，证明拓扑链接迫使弱有界几何流形上标量曲率多项式衰减，并发展局部于非紧致流形端点的障碍理论。

Manifolds with non-stable fundamental groups at infinity, II

In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with compact boundary, the condition of inward tameness has substatial implications for the algebraic topology at infinity. In particular, every inward tame manifold with compact boundary has stable homology (in all dimensions) and semistable fundamental group at each of its ends. In c…

Manifolds with non-stable fundamental groups at infinity, III

We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann's famous collaring theorem that applies to manifolds having non-stable fundamental group systems at infinity. In this paper a primary goal is finally achieved; namely, a complete characterization of pseudo-collarability for manifolds of dimension at least 6.

无穷远处的切锥

Tangent cones at infinity

本文定义并研究复代数集在无穷远处的两类切锥，证明纯维数条件可推出该代数集为仿射线性子空间，并将其与紧集外的分支覆盖表示联系起来，从而把 Whitney 和 Stutz 的经典结果推广到无穷远处。

Simplicial volume of closed locally symmetric spaces of non-compact type

We show that compact, locally symmetric spaces of non-compact type have positive simplicial volume. This gives a positive answer to a question that was first raised by Gromov in 1982. We provide a summary of results that are known to follow from positivity of the simplicial volume.