等变上同调与Čech超上同调的同构定理

杨海波

数学学报 ›› 2012, Vol. 55 ›› Issue (5) : 781-790.

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数学学报 ›› 2012, Vol. 55 ›› Issue (5) : 781-790. DOI: 10.12386/A2012sxxb0075
论文

等变上同调与Čech超上同调的同构定理

    杨海波1,2
作者信息 +

An Isomorphism Theorem Between Equivariant Cohomology and Čech Hypercohomology

    Hai Bo YANG1,2
Author information +
文章历史 +

摘要

首先证明了任意一个等变微分流形都存在等变良好开覆盖, 且等变良好开覆盖集所组成的集合在全部开覆盖组成的集合中共尾.在此基础上, 证明了等变上同调与Čech超 上同调的同构.此定理可应用于实代数簇的Deligne上同调研究.

Abstract

We first show that each equivariant smooth manifold has an equivariant good cover,and the equivariant good covers are cofinal in the set of open covers.We further this result to get an isomorphism theorem between equivariant cohomology and Čech hypercohomology.Such result can be applied to the study of Deligne cohomology of the real algebraic varieties.

关键词

等变上同调 / Čech超上同调 / 良好开覆盖

Key words

equivariant cohomology / Čech hypercohomology / good cover

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杨海波. 等变上同调与Čech超上同调的同构定理. 数学学报, 2012, 55(5): 781-790 https://doi.org/10.12386/A2012sxxb0075
Hai Bo YANG. An Isomorphism Theorem Between Equivariant Cohomology and Čech Hypercohomology. Acta Mathematica Sinica, Chinese Series, 2012, 55(5): 781-790 https://doi.org/10.12386/A2012sxxb0075

参考文献

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基金

国家自然科学天元青年基金(11126337);江西省教育厅青年科学基金(GJJ12442);江西省高校人文社科研究项目(JJ1239);南昌航空大学科研启动基金(EA201007057)
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