四维流形的对称群
几何拓扑
2007-07-26 v4 代数拓扑
群论
摘要
若一个（可能为有限的）紧李群在二阶贝蒂数至少为三的闭单连通四维流形上有效、局部线性且同调平凡地作用，则它必须同构于 S^1 x S^1 的一个子群，且该作用必须具有非空不动点集。我们的结果加强并补充了 Edmonds、Hambleton 和 Lee 以及 Wilczynski 等人的近期工作。我们的工具包括表示论、有限群论和 Borel 等变上同调。
引用
@article{arxiv.math/9907180,
title = {Symmetry groups of four-manifolds},
author = {Michael P. McCooey},
journal= {arXiv preprint arXiv:math/9907180},
year = {2007}
}
备注
This is a substantially revised and shortened version. The argument has been streamlined by a more natural organization of the "minimal bad" cases and a much simplified treatment of rank 2 nonabelian groups (such as the eight-element dihedral group) using results from "Four-manifolds which admit Z_p x Z_p actions" (math.GT/0002187). The main result has also been sharpened slightly by appeal to the G-signature theorem, and now covers manifolds with the cohomology of CP^2 # CP^2. 15 pages, LaTeX