S1上S1束的纤维保持映射的最小不动点集

IF 0.6 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-01-01 DOI:10.1016/j.topol.2024.109083

D.L. Gonçalves , A.K.M. Libardi , D. Vendrúscolo , J.P. Vieira

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引用次数: 0

摘要

在这项工作中，我们描述了S1-束在S1上的纤维映射的最小不动点集，直到纤维同伦。在这种条件下有两种振动，一种是可定向的，即环面，另一种是不可定向的，即克莱因瓶。对于光纤映射，最小不动点集可以为空，否则描述为不相交圆的有限并。我们给出了不动点集最小的模型，其中最小意味着在同一光纤同伦类中不动点集不存在任何适当的子集。

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On minimal fixed points set of fiber preserving maps of S1-bundles over S1

In this work, we describe the minimal fixed points set of fiberwise maps of

S^{1}

-bundles over

S^{1}

, up to fiberwise homotopies. There are two fibrations under these conditions, one orientable, the torus, and the other non-orientable, the Klein bottle. For fiberwise maps the minimal fixed points set can be empty, otherwise it is described as the finite union of disjoint circles. We present models for which the fixed points set are minimal, where minimal means that no proper subset can be realized as the fixed points set in the same fiberwise homotopy class.

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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.