动力系统的同调与K -理论2。具有完全不相连的横向的小空间

IF 0.7 2区数学 Q2 MATHEMATICS Journal of Noncommutative Geometry Pub Date : 2023-05-18 DOI:10.4171/jncg/494

Valerio Proietti, Makoto Yamashita

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引用次数: 0

摘要

将前人关于群拟同调与K -理论之间关系的研究成果应用于小空间。更确切地说，我们考虑了具有完全不连通稳定集的小空间的不稳定等价关系，并证明了相关谱序列在第二张表上显示了Putnam的稳定同调群。而且，这种同构实际上与不稳定等价关系的群拟同构。

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Homology and $K$-theory of dynamical systems II. Smale spaces with totally disconnected transversal

We apply our previous work on the relation between groupoid homology and $K$-theory to Smale spaces. More precisely, we consider the unstable equivalence relation of a Smale space with totally disconnected stable sets and prove that the associated spectral sequence shows Putnam's stable homology groups on the second sheet. Moreover, this homology is in fact isomorphic to the groupoid homology of the unstable equivalence relation.

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来源期刊

Journal of Noncommutative Geometry 数学-数学

CiteScore

1.60

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular: Hochschild and cyclic cohomology K-theory and index theory Measure theory and topology of noncommutative spaces, operator algebras Spectral geometry of noncommutative spaces Noncommutative algebraic geometry Hopf algebras and quantum groups Foliations, groupoids, stacks, gerbes Deformations and quantization Noncommutative spaces in number theory and arithmetic geometry Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.