# Hyperbolic Manifolds and Discrete Groups (Modern Birkhäuser Classics) download epub

#### by **Michael Kapovich**

**Epub Book:**1607 kb. |

**Fb2 Book:**1494 kb.

This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups .

This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on Thurston’s hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field

Автор: Michael Kapovich Название: Hyperbolic Manifolds and Discrete Groups Издательство: Springer . Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology.

Both authors have published extensively in the general area of discrete groups, hyperbolic manifolds and low-dimensional topology.

The simplest example of a hyperbolic manifold is Hyperbolic space, as each point in hyperbolic space has a. .

The simplest example of a hyperbolic manifold is Hyperbolic space, as each point in hyperbolic space has a neighborhood isometric to hyperbolic space. Kapovich, Michael (2009), Hyperbolic manifolds and discrete groups, Modern Birkhäuser Classics, Boston, MA: Birkhäuser Boston, doi:10. 5, ISBN 978-0-8176-4912-8, MR 1792613. Maclachlan, Colin; Reid, Alan W. (2003), The arithmetic of hyperbolic 3-manifolds, Graduate Texts in Mathematics, 219, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98386-8, MR 1937957.

Also presented are several deep theorems (and their proofs) about 3-manifolds and discrete groups .

Also presented are several deep theorems (and their proofs) about 3-manifolds and discrete groups: the Haken hierarchy theorem, Waldhausen's homeomorphism theorem, Bonahon's theorem, Ahlfors finiteness theorem, and Sullivan's rigidity theorem. Hyperbolic Manifolds and Discrete Groups is replete with beautiful illustrations and examples of key concepts. It should serve as a comprehensive reference for mathematicians and students or as a text for a graduate seminar. The main focus throughout the text is on Thurston's hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field.

This classic book is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups . The main focus throughout the text is on Thurston’s hyperbolization theorem, one of the central results of 3-dimensional topology that has completely changed the landscape of the field

The meat of Thurston’s proof can be found in two books: Michael Kapovich’s Hyperbolic Manifolds and Discrete Groups and .

The meat of Thurston’s proof can be found in two books: Michael Kapovich’s Hyperbolic Manifolds and Discrete Groups and . Otal’s Le théorème d& pour les vari’tés fibrées de dimension 3. The precise theorem that these books (jointly) prove is: Hyperbolization Theorem: Suppose that M is a compact atoroidal Haken 3-manifold that has zero Euler characteristic. Then the interior of M is the quotient of hyperbolic 3-space by a discrete group of isometries.

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some .

In mathematics, a hyperbolic manifold is a space where every point looks locally like hyperbolic space of some dimension. They are especially studied in dimensions 2 and 3, where they are called hyperbolic surfaces and hyperbolic 3-manifolds, respectively. In these dimensions, they are important because most manifolds can be made into a hyperbolic manifold by a homeomorphism.

Find many great new & used options and get the best deals for Hyperbolic Manifolds and Discrete Groups by.The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index.

The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index.

Hyperbolic Manifolds and Discrete Groups is at the crossroads of several branches of mathematics: hyperbolic geometry, discrete groups, 3-dimensional topology, geometric group theory, and complex analysis. The main focus throughout the text is on the "Big Monster," i.e., on Thurston’s hyperbolization theorem, which has not only completely changes the landscape of 3-dimensinal topology and Kleinian group theory but is one of the central results of 3-dimensional topology.

The book is fairly self-contained, replete with beautiful illustrations, a rich set of examples of key concepts, numerous exercises, and an extensive bibliography and index. It should serve as an ideal graduate course/seminar text or as a comprehensive reference.

**Author:**Michael Kapovich

**ISBN:**0817649123

**Category:**Science & Math

**Subcategory:**Mathematics

**Language:**English

**Publisher:**Birkhäuser; 2010 edition (October 28, 2009)

**Pages:**470 pages