Gyration stability for projective planes

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-05-08 DOI:10.1016/j.topol.2025.109420

Sebastian Chenery , Stephen Theriault

引用次数: 0

Abstract

Gyrations are operations on manifolds that arise in geometric topology, where a manifold M may exhibit distinct gyrations depending on the chosen twisting. For a given M, we ask a natural question: do all gyrations of M share the same homotopy type regardless of the twisting? A manifold with this property is said to have gyration stability. Inspired by recent work by Duan, which demonstrated that the quaternionic projective plane is not gyration stable with respect to diffeomorphism, we explore this question for projective planes in general. We obtain a complete description of gyration stability for the complex, quaternionic, and octonionic projective planes up to homotopy.

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射影平面的旋转稳定性

旋转是对几何拓扑中出现的流形的操作，其中流形M可能表现出不同的旋转，这取决于所选择的扭转。对于给定的M，我们问一个自然的问题：M的所有旋转是否都具有相同的同伦类型？具有这种性质的流形被称为具有旋转稳定性。受Duan最近工作的启发，证明了四元数射影平面在微分同构方面不是旋转稳定的，我们在一般的射影平面上探讨了这个问题。我们得到了直至同伦的复平面、四元数平面和八元数平面的旋转稳定性的完整描述。

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.