A study of the Ganea conjecture for topological complexity by using weak topological complexity

TL;DR

This paper investigates the Ganea conjecture for topological complexity by utilizing weak topological complexity and its stable variant, providing new conditions and examples for when the conjecture holds.

Contribution

It introduces sufficient conditions involving weak topological complexity for the Ganea conjecture to be satisfied, expanding understanding of topological complexity.

Findings

Identifies conditions under which the Ganea conjecture holds

Uses auxiliary invariants to analyze topological complexity

Provides examples illustrating the theoretical results

Abstract

In this paper, we provide sufficient conditions for a space $X$ to satisfy the Ganea conjecture for topological complexity. To achieve this, we employ two auxiliary invariants: weak topological complexity in the sense of Berstein-Hilton, along with a certain stable version of it. Several examples are discussed