# Topological complexity of classical configuration spaces and related objects

## TL;DR

This paper surveys the topological complexity of classical configuration spaces on surfaces and related spaces, highlighting recent results and connections to algebraic and geometric properties.

## Contribution

It provides a comprehensive overview of the topological complexity in various configuration spaces, including orbit spaces and Eilenberg-Mac Lane spaces, linking topology with group actions.

## Key findings

- Topological complexity varies with surface genus and configuration type.
- Connections established between configuration space topology and algebraic properties of associated groups.
- Survey consolidates known results and identifies open problems in the field.

## Abstract

We survey results on the topological complexity of classical configuration spaces of distinct ordered points in orientable surfaces and related spaces, including certain orbit configuration spaces and Eilenberg-Mac Lane spaces associated to certain discrete groups.