# Multidimensional topological Galois theory

## TL;DR

This paper outlines a multidimensional extension of topological Galois theory, exploring topological obstructions to solving equations in finite terms, based on the author's book and aimed at enriching classical integration theory.

## Contribution

It introduces a multidimensional framework for topological Galois theory, expanding the classical theory to higher dimensions and providing foundational definitions and results.

## Key findings

- Defines multidimensional topological Galois groups
- Identifies obstructions to solvability in finite terms
- Provides a basis for further research in multidimensional integration

## Abstract

In this preprint we present an outline of the multidimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvability by radicals, by elementary functions, by quadratures and so on). This 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. This 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.