On exotic algebraic structures on affine spaces

TL;DR

This paper surveys recent developments in exotic algebraic structures on affine spaces, focusing on their analytic properties and highlighting open problems in the field.

Contribution

It provides a comprehensive overview of recent progress and open questions regarding exotic algebraic structures on affine spaces, emphasizing their analytic aspects.

Findings

Identification of exotic structures diffeomorphic to ${f R}^{2n}$

Emphasis on analytic properties of these structures

Highlighting open problems in the field

Abstract

By an exotic algebraic structure on the affine space ${\bf C}^n$ we mean a smooth affine algebraic variety which is diffeomorphic to ${\bf R}^{2n}$ but not isomorphic to ${\bf C}^n$. This is a survey of the recent developement on the subject, which emphasizes its analytic aspects and points out some open problems.