G-分层伪流形的等变展开

F. Dalmagro

G-分层伪流形的等变展开

代数拓扑 2007-05-23 v1 一般拓扑

作者: F. Dalmagro

摘要

对于任意阿贝尔紧李群 $G$ ,我们引入一族 $G$ -分层伪流形,其主要特征是在分层伪流形范畴中保持轨道空间。这推广了 R. Popper 先前给出的定义。我们还找到了等变展开存在的一个充分条件,从而如 \cite{S} 中所定义,拥有带微分形式的相交上同调。此外,若 $G$ 作用于流形 $M$ ,我们找到 $M$ 的一个等变展开,它对 $G$ 的每个闭子群 $K$ 在 $k$ -轨道空间上诱导一个典范展开。

关键词

等变展开 G-分层伪流形阿贝尔紧李群相交上同调轨道空间

引用

@article{arxiv.math/0312213,
  title  = {Equivariant Unfoldings of G-Stratified Pseudomanifolds},
  author = {F. Dalmagro},
  journal= {arXiv preprint arXiv:math/0312213},
  year   = {2007}
}

备注

This is a paper on geometric topology which generalizes in the stratified context the procedure of Davis for blowing up a smooth manifold along a closed submanifold. We also work in the equivariant category, generalizing a previous definition of R. Popper for $G$-stratified pseudomanifolds. The main applications of this work are intended to the cohomological study of torical actions on stratified pseudomanifolds, as a particular case of iterated stratified circle actions

G-分层伪流形的等变展开

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