# The real plane Cremona group is a non-trivial amalgam

## TL;DR

The paper proves that the real plane Cremona group is a non-trivial amalgamated product of two groups and provides an alternative proof of its abelianisation, advancing understanding of its algebraic structure.

## Contribution

It establishes the non-trivial amalgamated structure of the real plane Cremona group and offers a new proof of its abelianisation, contributing to algebraic geometry and group theory.

## Key findings

- The real plane Cremona group is a non-trivial amalgam.
- An alternative proof of its abelianisation is provided.
- The group’s structure is clarified as an amalgamated product.

## Abstract

We show that the real Cremona group of the plane is a non-trivial amalgam of two groups amalgamated along their intersection and give an alternative proof of its abelianisation.