Update Log :

• Latest version is from January 28, 2023 [work in progress; some index entries added, Ch 1 improved, Bibliography improved]

This is the celebrated Green Book on geometric group theory edited by Etienne Ghys and Pierre de la Harpe. The original title is in French. It is inaccessible for students whose primary means of accessing knowledge is English. Here I am referring more to non-native English speakers, who have already gone through the process of learning a second language to explore the mathematical world.

W.E. Grosso has a rough translation of this book. His work is available online for free. However the copy that we found goes up to Chapter ?? of the Springer title `About Hyperbolic Groups after Mikhail Gromov'. In this volume we have covered the entire book.

This project was taken up in the student research seminar at Cheentan Research Foundation. This continues to be a work in progress as we dig deeper into each of the chapters. The following students participated in the process.

• Soumyadip Kar
• Supriti Laha
• Subhadip Banerjee
• J V Raghunath

Subarna Ghosh and Chalsi Garg helped in proof reading and fine tuning the content.

When we began this reading project the students knew almost no French. The group started learning French, using google translate and AI driven OCR softwares. All student participants were advanced undergraduates or early graduate school students with limited understanding of geometric group theory. Therefore they had to learn the basics of this vast subject. At any rate this has been a labor of love through barriers of language and concept.

We did not include the Appendix from the Springer version (on small cancellation groups by Ralph Strabel) as it is written in English. However we did include the Chapter 10 of Springer edition for the sake of continuity (though it is in English as well).

We have included some short notes at the end of the book. We call these notes `blogs'. They contain certain musings with the content. More of these will be added in future versions of this volume. These notes emerged from our weekly discussions and reading activity.

Apart from translation, we have also included some remarks in the margin. We foresee that the number of remarks will continue to grow in future.

In fact the reader will readily notice that the margin is considerably thicker than usual. Most of these comments were part of expanded discussions while working through the chapters. The goal of the marginalia is to be a cheerful companion for the reader. These are echoes from a not-so-distant past when a happy set of learners struggled through these ideas at late hours week after week. The comments in the marginalia includes several other references. Hence the bibliography of this volume is larger than that of the original text.

We think that some beginners in the field of geometric group theory may find this translation useful. Hence we have made a free copy available in the internet with the sole objective sharing knowledge.

Let us know if you find errors or have suggestions for improvement.

Thank you,

Ashani Dasgupta
Cheentan Research Foundation
Calcutta, 2022
ashani.dasgupta@cheenta.com

This is a work in progress. Check back for newer and more improved versions. New versions are usually uploaded every month.