# Q-Topological Complexity

## TL;DR

This paper introduces new topological invariants called Q-sectional category and Q-topological complexity, generalizing classical concepts and providing formulas for their behavior in fibrations, enriching the understanding of topological complexity.

## Contribution

It defines the invariants Q-sectional category and Q-topological complexity, establishing their properties and a generalized formula for their behavior in fibrations.

## Key findings

- Introduced Q-sectional category and Q-topological complexity.
- Established properties of these invariants.
- Derived a generalized formula for fibrations.

## Abstract

By analogy with the invariant Q-category defined by Scheerer, Stanley and Tanr\'e, we introduce the notions of Q-sectional category and Q-topological complexity. We establish several properties of these invariants. We also obtain a formula for the behaviour of the sectional category with respect to a fibration which generalizes the classical formulas for Lusternik-Schnirelmann category and topological complexity.