Computations in rational sectional category

TL;DR

This paper provides new bounds and methods for computing rational sectional category and topological complexity of formal spaces, linking these invariants to cohomology for simplified calculations.

Contribution

It introduces simple upper bounds for rational sectional category and a method to compute higher topological complexity using cohomology of formal spaces.

Findings

Sectional category of formal morphisms reaches its cohomological lower bound.

Method to compute higher topological complexity from cohomology.

Provides bounds and computations for invariants of rational spaces.

Abstract

We give simple upper bounds for rational sectional category and use them to compute invariants of the type of Farber's topological complexity of rational spaces. In particular we show that the sectional category of formal morphisms reaches its cohomological lower bound and give a method to compute higher topological complexity of formal spaces in terms of their cohomology.