Last edited by Bashura
Monday, July 13, 2020 | History

7 edition of The Arithmetic of Hyperbolic 3-Manifolds found in the catalog.

The Arithmetic of Hyperbolic 3-Manifolds

by Colin Maclachlan

  • 118 Want to read
  • 10 Currently reading

Published by Springer .
Written in English


The Physical Object
Number of Pages480
ID Numbers
Open LibraryOL7449662M
ISBN 100387983864
ISBN 109780387983868

Arithmetic of hyperbolic 3-manifolds. Book. Aug ; Lect Notes Math It is a long standing conjecture that all closed P 2-irreducible 3-manifolds with infinite fundamental group have Author: Igor Nikolaev. arithmetic subgroups of PSL(2,C). These manifolds often seem to have special beauty. Many of the key examples in the development of the theory of geometric structures on 3-manifolds (e.g. the figure-eight knot complement, the Whitehead link complement, the complement of the Borromean rings and the Magic manifold) are arithmetic.

Buy The Arithmetic of Hyperbolic 3-Manifolds by Colin MacLachlan, Alan W. Reid online at Alibris. We have new and used copies available, in 2 editions - starting at $ Shop now. Table of Contents. Front/Back Matter. View this volume's front and back matter; Articles. Joel Hass – What is an Almost Normal Surface? Danny Calegari – The Ergodic Theory of Hyperbolic Groups Sungbok Hong and Darryl McCullough – Mapping Class Groups of $3$-Manifolds, Then and Now B. H. Bowditch – Stacks of Hyperbolic Spaces and Ends of 3-Manifolds.

Arithmetic hyperbolic 3-manifolds, perfectoid spaces, and Galois representations I - Peter Scholze. Peter Scholze. University of Bonn. Febru One of the most studied objects in mathematics is the modular curve, which is the quotient of hyperbolic . This book is an exposition of the theoretical foundations of hyperbolic manifolds. It is intended to be used both as a textbook and as a reference. This third edition greatly expands upon the second with an abundance of additional content, including a section dedicated to arithmetic hyperbolic groups.


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The Arithmetic of Hyperbolic 3-Manifolds by Colin Maclachlan Download PDF EPUB FB2

"This is a book of great importance on the theory of hyperbolic manifolds (and Kleinian groups) since it is the first to provide a complete, precise, clearly-written and self-contained exposition of the arithmetic aspects of the theory.

For this, the book fills a void in the mathematics literature concerning hyperbolic by: While there are a number of texts that cover the topological, geometric, and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts." (L’ENSEIGNEMENT MATHEMATIQUE, Vol.

49, (), ) From the Back Cover/5(3). While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts. This book gives a fantastic explanation of the state of the art (as of ) on the study of hyperbolic 3-manifolds using arithmetic invariants.

It is an essential tool for anyone working in that /5(2). "This is a book of great importance on the theory of hyperbolic manifolds (and Kleinian groups) since it is the first to provide a complete, precise, clearly-written and self-contained exposition of the arithmetic aspects of the theory.

For this, the book fills a void in the mathematics The Arithmetic of Hyperbolic 3-Manifolds book concerning hyperbolic geometry/5(2).

Arithmetic of Hyperbolic Three-Manifolds Colin Maclachlan, Alan W. Reid Recently there has been considerable interest in developing techniques based on number theory to attack problems of 3-manifolds; Contains many examples and lots of problems; Brings together much of the existing literature of Kleinian groups in a clear and concise way; At.

Download The geometry and topology of arithmetic hyperbolic 3-manifolds book pdf free download link or read online here in PDF. Read online The geometry and topology of arithmetic hyperbolic 3-manifolds book pdf free download link book now. All books are in clear copy here, and all files are secure so don't worry about it.

By a hyperbolic 3-manifold we mean a complete orientable hyperbolic 3-manifold of finite volume, that is a quotient H3= with ˆ PSL2C a discrete subgroup of finite covolume (here briefly “a Kleinian group”).

Among hyperbolic 3-manifolds, the arithmetic ones form an interesting, and in many ways more tractable, subclass. Maclachlan / Reid, The Arithmetic of Hyperbolic 3-Manifolds, 1st Edition. Softcover version of original hardcover edition, Buch, Bücher schnell und portofrei.

Moreover, the existence part of the classification theorem for quaternion algebras (Theorem ) gives the existence of arithmetic Kleinian groups satisfying a variety of conditions, which, in turn, give the existence of hyperbolic 3-manifolds and orbifolds with a range of topological and geometric properties.

"This is a book of great importance on the theory of hyperbolic manifolds (and Kleinian groups) since it is the first to provide a complete, precise, clearly-written and self-contained exposition of the arithmetic aspects of the theory. For this, the book fills a void in the mathematics literature concerning hyperbolic.

Maclachlan / Reid, The Arithmetic of Hyperbolic 3-Manifolds,Buch, Bücher schnell und portofrei. The construction of arithmetic Kleinian groups from quaternion algebras gives rise to particularly interesting hyperbolic manifolds.

On the other hand they are in some sense "rare" among hyperbolic 3-manifolds (for example hyperbolic Dehn surgery on a fixed manifold results in a non-arithmetic manifold for almost all parameters).

Arithmetic of Hyperbolic 3-Manifolds Alan Reid Rice University. Hyperbolic 3-Manifolds and Discrete Groups Hyperbolic 3-space can be de ned as H3 = f(z;t) 2C R: t>0g and equipped with the metric ds= ds E t. Geodesics are vertical lines perpendicular to C or semi-circles perpendicular to C.

This heavily class-tested book is an exposition of the theoretical foundations of hyperbolic manifolds. It is a both a textbook and a reference.

A basic knowledge of algebra and topology at the first year graduate level of an American university is assumed. The first part is concerned with hyperbolic geometry and discrete groups.

Arithmetic of Hyperbolic 3-Manifolds. Support. Adobe DRM ( / – 2 customer ratings) While there are a number of texts which cover the topological, geometric and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts.

This result has number-theoretic significance explained in Appendix B [81]. More deeply, theory of arithmetic hyperbolic 3-manifolds is explained in the book by [91].

Some physical (cosmological. Arithmetic Hyperbolic 3-Manifolds and Orbifolds. Bianchi Groups. Arithmetic Link Complements.

Zimmert Sets and Cuspidal Cohomology. The Arithmetic Knot. From the reviews:"In this book Machlachlan and Reid give a comprehensive treatment of hyperbolic 3-manifolds and Kleinian groups from the viewpoint of algebraic.

This book introduces and explains hyperbolic geometry and hyperbolic 3- and 2-dimensional manifolds in the first two chapters and then goes on to develop the subject. The author discusses the profound discoveries of the astonishing features of these 3-manifolds, helping the reader to understand them without going into long, detailed formal proofs.

The present book is a comprehensive guide to theories of Kleinian groups from the viewpoints of hyperbolic geometry and complex analysis.

AfterAhlfors and Bers were the leading researchers of Kleinian groups and helped it to become an active area of. While there are a number of texts that cover the topological, geometric, and analytical aspects of hyperbolic 3-manifolds, this book is unique in that it deals exclusively with the arithmetic aspects, which are not covered in other texts." (L'ENSEIGNEMENT MATHEMATIQUE, Vol.

49, (), ) Read .On the arithmetic and geometry of binary Hamiltonian forms Parkkonen, Jouni and Paulin, Frédéric, Algebra & Number Theory, ; Cheeger constants of arithmetic hyperbolic 3-manifolds Lanphier, Dominic and Rosenhouse, Jason, Illinois Journal of Mathematics, ; Geometry and rank of fibered hyperbolic $3$–manifolds Biringer, Ian, Algebraic & Geometric Topology, lattice subgroup of hyperbolic isometries.

This quotient is a manifold if the group is torsion-free. For example, the volume of a smooth hyperbolic surface is always an integral multiple of 2ˇand the volume spectrum of hyperbolic 3-manifolds is a well-ordered subset of the real numbers.

Siegel’s problem asks for the minimal volume hyperbolic.