映射的相对 LS 范畴与高阶拓扑复杂度
代数拓扑
2021-12-03 v1
摘要
本文研究映射的三种相对 LS 范畴,并探讨它们的一些性质。随后我们引入映射的“高阶拓扑复杂度”与“弱高阶拓扑复杂度”。它们均为同伦不变量。我们讨论了这些不变量的一些下界与上界,并将其与先前已知的映射的“拓扑复杂度”进行比较。
引用
@article{arxiv.2112.00983,
title = {Relative LS categories and higher topological complexities of maps},
author = {Yuli B. Rudyak and Soumen Sarkar},
journal= {arXiv preprint arXiv:2112.00983},
year = {2021}
}
备注
The paper arXiv:2011.13531 is subdivided in two parts. The article containing the results of Sections 4 and 5 is accepted in Topological methods in nonlinear analysis. This current version is an expansion of Sections 2 and 3 as well as the concept of weak higher TC of maps has been added. 17 pages