Translation project on 'About Hyperbolic Groups after Mikhail Gromov' by Etienne Ghys and Pierre de la Harpe

Update Log :

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.

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 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, India

May, 2024

The final draft uploaded on 12th May was taken down due to a communication received from Springer.

Progress Report.

Connectedness of Bowditch boundary of Dehn fillings

We study Dehn fillings of relatively hyperbolic group pairs (\Gamma, \P) and the persistence of connectedness of Bowditch boundary in sufficiently long Dehn fillings. We show that the restriction of peripheral subgroups to virtually polycyclic subgroups (as in [Groves-Manning, 2018]) is not needed.

Download the preprint here.