Involutions on the product of projective space and sphere

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-06-19 DOI:10.1016/j.topol.2025.109481

Dimpi , Hemant Kumar Singh

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引用次数: 0

Abstract

This paper focuses on the actions of

G = Z_{2}

on a finite CW-complex X, whose mod 2 cohomology is isomorphic to that of a product of projective space and sphere,

F P^{n} \times S^{m}

, where

F

is either

R

C

. For the case when X is totally nonhomologous to zero in

X_{G}

, we determine the possible connected fixed point sets and construct examples illustrating these possibilities. We also address the case when X is not totally nonhomologous to zero in

X_{G}

under certain assumptions.

Furthermore, we compute the cohomology ring structure of the orbit spaces of free involutions on X. As an application, we derive the Borsuk-Ulam type results.

查看原文本刊更多论文

射影空间与球积的对合

本文研究了G=Z2在有限cw -复X上的作用，该复X的模2上同构于射影空间与球的乘积FPn×Sm，其中F为R或c。对于X在XG中完全不同构于0的情况，我们确定了可能的连通不动点集，并构造了说明这些可能性的例子。我们还讨论了在某些假设下，X在XG中不完全不同源于零的情况。进一步，我们计算了x上自由对合轨道空间的上同环结构。作为应用，我们得到了Borsuk-Ulam型结果。

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

Topology and its Applications 数学-数学

CiteScore

1.20

自引率

33.30%

发文量

251

审稿时长

6 months

期刊介绍： Topology and its Applications is primarily concerned with publishing original research papers of moderate length. However, a limited number of carefully selected survey or expository papers are also included. The mathematical focus of the journal is that suggested by the title: Research in Topology. It is felt that it is inadvisable to attempt a definitive description of topology as understood for this journal. Certainly the subject includes the algebraic, general, geometric, and set-theoretic facets of topology as well as areas of interactions between topology and other mathematical disciplines, e.g. topological algebra, topological dynamics, functional analysis, category theory. Since the roles of various aspects of topology continue to change, the non-specific delineation of topics serves to reflect the current state of research in topology. At regular intervals, the journal publishes a section entitled Open Problems in Topology, edited by J. van Mill and G.M. Reed. This is a status report on the 1100 problems listed in the book of the same name published by North-Holland in 1990, edited by van Mill and Reed.