Free and properly discontinuous actions of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1*_{G_0}G_2\)

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2016-10-18 DOI:10.1007/s40062-016-0158-7

Marek Golasiński, Daciberg Lima Gonçalves

引用次数: 2

Abstract

We estimate the number of homotopy types of orbit spaces for all free and properly discontinuous cellular actions of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1*_{G_0}G_2\). In particular, homotopy types of orbits of \((2n-1)\)-spheres \(\Sigma (2n-1)\) for such actions are analysed, provided the groups \(G_0, G_1, G_2\) and G are finite and periodic. This family of groups \(G\rtimes {\mathbb {Z}}^m\) and \(G_1*_{G_0}G_2\) contains properly the family of virtually cyclic groups. The possible actions of those groups on the top cohomology of the homotopy sphere are determined as well.

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自由和适当间断的团体行动\(G\rtimes {\mathbb {Z}}^m\)和 \(G_1*_{G_0}G_2\)

我们估计了群\(G\rtimes {\mathbb {Z}}^m\)和\(G_1*_{G_0}G_2\)的所有自由和适当不连续的细胞作用的轨道空间同伦类型的数目。特别地，在\(G_0, G_1, G_2\)群和G群是有限周期群的情况下，分析了该类作用的\((2n-1)\) -球\(\Sigma (2n-1)\)轨道的同伦类型。这个族\(G\rtimes {\mathbb {Z}}^m\)和\(G_1*_{G_0}G_2\)包含了虚拟循环族。并确定了这些群在同伦球上同调上的可能作用。

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

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.