# On Double Danielewski Surfaces and the Cancellation Problem

## TL;DR

This paper investigates a specific family of affine surfaces that serve as counter-examples to the Cancellation Problem, analyzing their invariants, isomorphism classes, and automorphisms to deepen understanding of these complex structures.

## Contribution

The paper provides a detailed description of the Makar-Limanov invariant, classifies the surfaces up to isomorphism, and characterizes their automorphism groups.

## Key findings

- Identified the Makar-Limanov invariant for the surfaces.
- Classified the surfaces into isomorphism classes.
- Characterized the automorphism groups of the surfaces.

## Abstract

We study a two-dimensional family of affine surfaces which are counter-examples to the Cancellation Problem. We describe the Makar-Limanov invariant of these surfaces, determine their isomorphism classes and characterize the automorphisms of these surfaces.