Higher Topological Complexity For Fibrations

TL;DR

This paper introduces the concept of higher topological complexity for fibrations, exploring its properties and relationships with existing topological invariants, and establishing that it is invariant under fiber homotopy equivalence.

Contribution

It defines higher topological complexity for fibrations via two approaches and proves its invariance under fiber homotopy equivalence, extending the understanding of topological invariants.

Findings

Higher topological complexity (TC_{n}) can be defined via homotopic distance and Schwarz genus.

TC_{n} of a fibration is invariant under fiber homotopy equivalence.

Results relate TC_{n} to classical invariants like TC and cat.

Abstract

We introduce the higher topological complexity (TC_{n}) of a fibration in two ways: the higher homotopic distance and the Schwarz genus. Then we have some results on this notion related to TC, TC_{n} or cat of a topological space or a fibration. We also show that TC_{n} of a fibration is a fiber homotopy equivalence.