# Quotients and invariants of AS-sets equipped with a finite group action

## TL;DR

This paper introduces invariants for real algebraic sets with finite group actions using geometric quotients, aiding in classifying these sets up to equivariant homeomorphisms.

## Contribution

It develops new invariants for GAS sets under finite group actions based on geometric quotients and AS-graph structures, including additive invariants with integer values.

## Key findings

- Constructed invariants of GAS sets using geometric quotients.
- Established invariants are preserved under equivariant homeomorphisms.
- Defined additive invariants with values in Z.

## Abstract

Using the geometric quotient of a real algebraic set by the action of a finite group G, we construct invariants of GAS sets with respect to equivariant homeomorphisms with AS-graph, including additive invariants with values in Z.