Madsen-Weiss 定理简述
几何拓扑
2014-02-11 v2 代数拓扑
摘要
本文是对Madsen-Weiss定理证明的阐述，该定理断言，在稳定维数范围内，曲面的映射类群的上同调与通过“扫描方法”自然产生的某个无穷环路空间的上同调同构。这里给出的证明利用了Galatius和Randal-Williams引入的简化方法。
关键词
引用
@article{arxiv.1103.5223,
title = {A short exposition of the Madsen-Weiss theorem},
author = {Allen Hatcher},
journal= {arXiv preprint arXiv:1103.5223},
year = {2014}
}
备注
Version 2 adds three appendices containing background material: (1) Gramain's proof of the Earle-Eells theorem on contractibility of the components of diffeomorphism groups of surfaces, (2) the calculation of the stable rational homology, and (3) a proof of the Group Completion Theorem following an argument of Galatius. The exposition of the paper has also been reorganized significantly