Surface Groups In The Group Of Germs Of Analyticdiffeomorphisms In One Variable

TL;DR

This paper constructs embeddings of surface groups into the group of germs of analytic diffeomorphisms in one variable, advancing understanding of the algebraic structure of these transformation groups.

Contribution

It introduces a method to embed surface groups into the group of germs of analytic diffeomorphisms, providing new insights into their algebraic and geometric properties.

Findings

Successful embedding of surface groups demonstrated

New techniques for analyzing germs of analytic diffeomorphisms

Enhanced understanding of the structure of transformation groups

Abstract

We construct embeddings of surface groups into the group of germs of analytic diffeomorphisms in one variable.