等变上同调为Cohen-Macaulay的环面作用
Torus actions whose equivariant cohomology is Cohen-Macaulay
摘要：
本文研究了Cohen-Macaulay作用，这是流形上一类可能没有不动点的环面作用，它推广了等变形式作用，并具有类似的性质。它们的等变上同调代数是可计算的，在这个意义上，一个张-Skjelbred引理，及其更强的版本，一个Atiyah-Bredon序列的正合性，持有。主要区别是用最低维轨道的并集代替了不动点集。我们找到了Cohen-Macaulay性质的充分条件，如存在不变的Morse-Bott函数，其临界集是最低维轨道的并，或轨道空间的开面无环性.专门针对环面流形的情况，即，r维环面作用于2 r维可定向紧流形，后者类似于Masuda和Panov的结果，也类似于Bredon的等变形式环面流形是开面非循环流形的逆结果.
英文摘要：
We study Cohen-Macaulay actions, a class of torus actions on manifolds, possibly without fixed points, which generalizes and has analogous properties as equivariantly formal actions. Their equivariant cohomology algebras are computable in the sense that a Chang-Skjelbred Lemma, and its stronger version, the exactness of an Atiyah-Bredon sequence, hold. The main difference is that the fixed point set is replaced by the union of lowest dimensional orbits. We find sufficient conditions for the Cohen-Macaulay property such as the existence of an invariant Morse-Bott function whose critical set is the union of lowest dimensional orbits, or open-face-acyclicity of the orbit space. Specializing to the case of torus manifolds, i.e., 2r-dimensional orientable compact manifolds acted on by r-dimensional tori, the latter is similar to a result of Masuda and Panov, and the converse of the result of Bredon that equivariantly formal torus manifolds are open-face-acyclic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
