# zbMATH — the first resource for mathematics

Foundations of hyperbolic manifolds. 3rd expanded edition. (English) Zbl 1430.51002
Graduate Texts in Mathematics 149. Cham: Springer (ISBN 978-3-030-31596-2/hbk; 978-3-030-31597-9/ebook). xii, 800 p. (2019).
The most significant changes in this edition are: (1) a more thorough development of the theory of crystallographic groups, to which three theorems have been added, (2) more finiteness properties of geometrically finite groups, with six new theorems, (3) the addition of an entire section on arithmetic hyperbolic groups, (4) an introduction to $$2$$-dimensional geometric orbifolds, as well as more results on compact geometric orbifolds, (5) almost all of the figures are now rendered in color, (6) the addition of 70 new exercises (solutions to all exercises in this edition will be made available in a solutions manual).

##### MSC:
 51-02 Research exposition (monographs, survey articles) pertaining to geometry 51M10 Hyperbolic and elliptic geometries (general) and generalizations 57M50 General geometric structures on low-dimensional manifolds 20H10 Fuchsian groups and their generalizations (group-theoretic aspects) 30F40 Kleinian groups (aspects of compact Riemann surfaces and uniformization) 57M60 Group actions on manifolds and cell complexes in low dimensions 57K35 Other geometric structures on 3-manifolds
Full Text: