Uniquely compatible transfer systems for cyclic groups of order prqs

IF 0.5 4区数学 Q3 MATHEMATICS

Topology and its Applications Pub Date : 2025-05-27 DOI:10.1016/j.topol.2025.109443

Kristen Mazur , Angélica M. Osorno , Constanze Roitzheim , Rekha Santhanam , Danika Van Niel , Valentina Zapata Castro

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引用次数: 0

Abstract

Bi-incomplete Tambara functors over a group G can be understood in terms of compatible pairs of G-transfer systems. In the case of

G = C_{p^{n}}

, Hill, Meng and Li gave a necessary and sufficient condition for compatibility and computed the exact number of compatible pairs. In this article, we study compatible pairs of G-transfer systems for the case

G = C_{p^{r} q^{s}}

and identify conditions when such transfer systems are uniquely compatible in the sense that they only form trivially compatible pairs. This gives us new insight into collections of norm maps that are relevant in equivariant homotopy theory.

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阶prqs循环群的唯一相容传递系统

群G上的双不完全Tambara函子可以用G转移系统的相容对来理解。在G=Cpn的情况下，Hill，孟和Li给出了相容的充分必要条件，并计算了相容对的确切数目。本文研究了G=Cprqs情况下G-传递系统的相容对，并确定了这种传递系统唯一相容的条件，即它们只形成平凡相容对。这使我们对等变同伦理论中相关的范数映射集合有了新的认识。

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.