Relative LS categories and higher topological complexities of maps
arXiv:2112.00983
Abstract
In this paper, we study three relative LS categories of a map and study some of their properties. Then we introduce the `higher topological complexity' and `weak higher topological complexity' of a map. Each of them are homotopy invariants. We discuss some lower and upper bounds of these in invariants and compare them with previously known `topological complexities' of a map.
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