等变 Poincaré-Alexander-Lefschetz 对偶性与 Cohen-Macaulay 性质
代数拓扑
2014-10-01 v3
摘要
我们证明了有理环面等变上同调与有理同调流形的 Poincaré-Alexander-Lefschetz 对偶性定理。我们允许非紧和非定向空间。我们利用此结论从等变同调中类似但更一般的短正合序列推导出等变上同调中的某些短正合序列，后者最初由 Duflot 在可微情形下提出。由轨道滤过产生的相对等变上同调模的 Cohen-Macaulay 性起到了关键作用。
引用
@article{arxiv.1303.1146,
title = {Equivariant Poincar\'e-Alexander-Lefschetz duality and the Cohen-Macaulay property},
author = {Christopher Allday and Matthias Franz and Volker Puppe},
journal= {arXiv preprint arXiv:1303.1146},
year = {2014}
}
备注
28 pages. This is a substantially expanded version of Section 6 of arXiv:1111.0957v1. v2: new result (Prop. 2.7) about equivariant homology in the case of freely acting subgroups; minor changes. v3: mistake in the proof of Prop. 2.7 corrected