# One dimensional topological Galois theory

## TL;DR

This paper outlines a one-dimensional topological Galois theory that investigates topological obstructions to solving equations in finite terms, based on the author's book and related to classical integration theory.

## Contribution

It introduces a new topological perspective on Galois theory for one-dimensional equations, extending classical algebraic approaches with topological concepts.

## Key findings

- Defines topological obstructions to solvability
- States key results and comments without proofs
- Connects to classical integration in finite terms

## Abstract

In the preprint we present an outline of the one dimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvabilty by radicals, by elementary functions, by quadratures and so on). The preprint is based on the author's book on topological Galois theory. It contains definitions, statements of results and comments to them. Basically no proofs are presented. The preprint was written as a part of the comments to a new edition (in preparation) of the classical book "Integration in finite terms'' by J.F.~Ritt. }