The Ganea conjecture for rational approximations of sectional category

TL;DR

This paper establishes bounds for the module sectional category of product maps, generalizes a theorem for Lusternik-Schnirelmann category, and advances the understanding of the Ganea conjecture for topological complexity in rational topology.

Contribution

It provides new bounds for module sectional category of product maps and proves a Ganea type conjecture for topological complexity in the rational setting.

Findings

Bounds for module sectional category of product maps

Proof of Ganea type conjecture for topological complexity

Progress towards Ganea conjecture in rational topology

Abstract

We give bounds for the module sectional category of products of maps which generalise a theorem of Jessup for Lusternik-Schnirelmann category. We deduce also a proof of a Ganea type conjecture for topological complexity. This is a first step towards proving the Ganea conjecture for topological complexity in the rational context.