发表机构
Indian Institute of Technology Madras; Indian Institute of Technology Bombay（印度理工学院马德拉斯分校; 印度理工学院孟买分校）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对G-映射引入等变相对截面范畴，建立其同伦性质，将其应用于定义映射拓扑复杂度等变类似物等，证明相关不变量扩展了经典等变概念。
AI 中文摘要
相对截面范畴由González、Grant和Vandembroucq针对纤维化引入，后被García-Calcines扩展到任意映射，它提供了一个包含多个数值同伦不变量的统一框架，包括Lusternik–Schnirelmann范畴、映射的拓扑复杂度和同伦距离。本文针对G-映射引入并研究相对截面范畴的等变类似物，建立其基本同伦理论性质，包括比较、乘积和合成不等式，以及其在定义域和陪域变化下的行为。作为应用，我们引入并研究Scott和Murillo–Wu意义下的映射拓扑复杂度的等变类似物，以及映射的等变Lusternik–Schnirelmann范畴，提供若干例子阐释该理论并证明这些不变量扩展了相应的经典等变概念。
英文摘要
The relative sectional category, introduced by González, Grant, and Vandembroucq for fibrations and later extended by García-Calcines to arbitrary maps, provides a common framework encompassing several numerical homotopy invariants, including the Lusternik--Schnirelmann category, the topological complexity of a map, and homotopic distance. In this paper, we introduce and study the equivariant analogue of the relative sectional category for $G$-maps. We establish its fundamental homotopy-theoretic properties, including comparison, product, and composition inequalities, as well as its behavior under changes of domain and codomain. As applications, we introduce and investigate equivariant analogues of the topological complexity of a map, in the sense of Scott and Murillo--Wu, and the equivariant Lusternik--Schnirelmann category of a map. Several examples are provided to illustrate the theory and demonstrate that these invariants extend the corresponding classical equivariant notions.
CommentsRevised version. Several corrections and clarifications have been made
