(ℤ2 ⊕ ℤ2)对称空间上各向同性作用的等变形式性

IF 0.5 3区 数学 Q3 MATHEMATICS Journal of Topology and Analysis Pub Date : 2023-12-14 DOI:10.1142/s1793525323500504
Manuel Amann, Andreas Kollross
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引用次数: 0

摘要

紧凑对称空间可能是最突出的一类形式空间,即有理同调类型是有理同调代数的形式结果的空间。作为一般化,我们甚至知道它们的等向作用是等变形式的。在本文中,我们证明了(ℤ2⊕ℤ2)对称空间是等变形式的,尤其是在沙利文的意义上是形式的。此外,我们用新方法给出了对称空间等变形式性的简短替代证明。
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Equivariant formality of the isotropy action on (ℤ2 ⊕ ℤ2)-symmetric spaces

Compact symmetric spaces are probably one of the most prominent class of formal spaces, i.e. of spaces where the rational homotopy type is a formal consequence of the rational cohomology algebra. As a generalization, it is even known that their isotropy action is equivariantly formal. In this paper, we show that (22)-symmetric spaces are equivariantly formal and formal in the sense of Sullivan, in particular. Moreover, we give a short alternative proof of equivariant formality in the case of symmetric spaces with our new approach.

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来源期刊
CiteScore
1.50
自引率
0.00%
发文量
13
审稿时长
>12 weeks
期刊介绍: This journal is devoted to topology and analysis, broadly defined to include, for instance, differential geometry, geometric topology, geometric analysis, geometric group theory, index theory, noncommutative geometry, and aspects of probability on discrete structures, and geometry of Banach spaces. We welcome all excellent papers that have a geometric and/or analytic flavor that fosters the interactions between these fields. Papers published in this journal should break new ground or represent definitive progress on problems of current interest. On rare occasion, we will also accept survey papers.
期刊最新文献
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