Deformation theory of discontinuous groups : geometry of Clifford-Klein forms, local rigidity, and stability concepts / Ali Baklouti.

Format:

Book

Author/Creator:

Baklouti, Ali, author.

Series:

De Gruyter expositions in mathematics ; 0938-6572 volume 72.

De Gruyter expositions in mathematics , 0938-6572 ; volume 72

Language:

English

Subjects (All):

Discontinuous groups.

Mathematics.

Physical Description:

1 online resource (xiv, 430 pages) : illustrations.

Edition:

2nd edition.

Place of Publication:

Berlin ; Boston : De Gruyter, [2025]

Language Note:

In English.

Summary:

This project is a second edition of the textbook: Deformation Theory of Discontinuous Groups (De Gruyter 2022). It is devoted to studying various geometric and topological concepts related to the deformation and moduli spaces of discontinuous group actions, and building some interrelationships between these concepts. It presents full proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and researchers in Lie theory, discontinuous groups, and deformation spaces. A part of the first edition, the setting of affine actions is introduced and new ideas and methods are developed with full proofs. The setting of compact extensions is also re-written with new approaches and proofs. It also contains the most recent developments of the theory, extending from basic concepts to a comprehensive exposition, and highlighting the newest approaches and methods in deformation theory. It also includes the most recent solutions to many open questions over the last decades and brings related newest research results in this area. For specialists and beginners in deformation theory, the settings of Heisenberg and Threadlike cases are differently re-written with full details and proofs.

Contents:

Frontmatter

Preface

Contents

1 Structure theory and first basic concepts

2 Proper actions on solvable homogeneous spaces

3 Proper action for compact extensions

4 Proper action of affine discontinuous groups

5 Deformation and moduli spaces

6 Local rigidity and stability

7 Deforming in extensions of Heisenberg groups

8 Discontinuous actions in the threadlike setting

Bibliography

Index

Notes:

Includes bibliographical references and index.

Online resource; title from PDF title page (publisher's Web site, viewed 20. Mar 2025).

Other Format:

Print version: Baklouti, Ali Deformation theory of discontinuous groups.

ISBN:

9783111634340

3111634345

3111634329

9783111634326

OCLC:

1511482556

Publisher Number:

CIPO000203657

Access Restriction:

Restricted for use by site license