非球空间的序贯拓扑复杂度与子群包含的截面范畴。

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2025-01-01 Epub Date: 2024-11-09 DOI:10.1007/s00208-024-03033-1

Arturo Espinosa Baro, Michael Farber, Stephan Mescher, John Oprea

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引用次数: 0

摘要

我们将拓扑机器人学关于非球面空间拓扑复杂度（TC）的结果推广到在基本群水平上引起子群包含的振动的截面范畴。在此基础上，我们建立了非球空间的序贯TC的下界，以及表胚的参数化TC的下界。此外，我们将Costa-Farber规范类推广到序列TC的类，并探讨了它们的性质。我们将它们与非球面空间的顺序tc上的结果结合起来，得到不一定是非球面空间上的结果。

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Sequential topological complexity of aspherical spaces and sectional categories of subgroup inclusions.

We generalize results from topological robotics on the topological complexity (TC) of aspherical spaces to sectional categories of fibrations inducing subgroup inclusions on the level of fundamental groups. In doing so, we establish new lower bounds on sequential TCs of aspherical spaces as well as the parametrized TC of epimorphisms. Moreover, we generalize the Costa-Farber canonical class for TC to classes for sequential TCs and explore their properties. We combine them with the results on sequential TCs of aspherical spaces to obtain results on spaces that are not necessarily aspherical.

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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.