Minimal homeomorphisms and topological $K$-theory

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2020-12-20 DOI:10.4171/ggd/707

R. Deeley, I. Putnam, Karen R. Strung

引用次数: 4

Abstract

The Lefschetz fixed point theorem provides a powerful obstruction to the existence of minimal homeomorphisms on well-behaved spaces such as finite CW-complexes. We show that these obstructions do not hold for more general spaces. More precisely, minimal homeomorphisms are constructed on space with prescribed $K$-theory or cohomology. We also allow for some control of the map on $K$-theory and cohomology induced from these minimal homeomorphisms. This allows for the construction of many minimal homeomorphisms that are not homotopic to the identity. Applications to $C^*$-algebras will be discussed in another paper.

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极小同胚与拓扑K理论

Lefschetz不动点定理为良好行为空间（如有限CW复形）上的极小同胚的存在提供了有力的阻碍。我们表明，这些障碍物不适用于更一般的空间。更确切地说，极小同胚是用规定的$K$-理论或上同调在空间上构造的。我们还允许对$K$-理论上的映射和由这些最小同胚诱导的上同调进行一些控制。这允许构造许多对恒等式不是同宗的极小同胚。$C^*$-代数的应用将在另一篇论文中讨论。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.