# Group theory and three-dimensional manifolds

by John R. Stallings

Publisher: Yale University Press in New Haven

Written in English

## Subjects:

• Three-manifolds (Topology),
• Group theory

## Edition Notes

Bibliography: p. 63-64.

Classifications The Physical Object Statement by John Stallings. Series James K. Whittemore lectures in mathematics given at Yale University, Yale mathematical monographs ;, 4 LC Classifications QA613 .S7 Pagination v, 65 p. Number of Pages 65 Open Library OL5705038M ISBN 10 0300013973 LC Control Number 70151590

THE SMITH CONJECTURE The Equivariant Loop Theorem for Three-Dimensional Manifolds and a Review of the Existence Theorems for Minimal Surfaces Shing- Tung Yau* Department of Mathematics Stanford University Stanford, California and William H. Meeks, Ill lnstituto Mathematica Pura e Aplicada Rio d e Janeiro, Brazil The details of this chapter appeared in Meeks and Yau [4,5]. D. Cooper, C.D. Hodgson, S.P. Kerckhoff - Three-dimensional Orbifolds and Cone-Manifolds Reference 1 provides an overview of the topic and is a complete . Get this from a library! Algebraic K-theory of crystallographic groups: the three-dimensional splitting case. [Daniel Scott Farley; Ivonne Johanna Ortiz] -- The Farrell-Jones isomorphism conjecture in algebraic K-theory offers a description of the algebraic K-theory of a group using a generalized homology theory. In cases where the conjecture is known to. This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures.

Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM), Volume - Ebook written by David Eisenbud, Walter D. Neumann. Read this book using Google Play Books app on your PC, android, iOS devices. Download for offline reading, highlight, bookmark or take notes while you read Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. The goal of this book is to characterize algebraically the closed 4-manifolds that fibre nontrivially or admit geometries in the sense of Thurston, or which are obtained by surgery on 2-knots, and. M-theory is a theory in physics that unifies all consistent versions of superstring theory. Edward Witten first conjectured the existence of such a theory at a string-theory conference at the University of Southern California in the spring of Witten's announcement initiated a flurry of research activity known as the second superstring revolution. The first three of these are related to knot theory, while the fourth makes use of differential geometry. We will also study Seifert fibrations and enumerate the eight 3-dimensional geometries. One goal is to understand the importance of Thurston's geometrization conjecture for the classification of 3-manifolds.

computing. It is a modiﬂed version of Chapter 14 of our book [18] and an expanded version of [58]. Quantum topology is, roughly speaking, that part of low-dimensional topology that interacts with statistical and quantum physics. Many invariants of knots, links and three dimensional manifolds have been. non semisimple topological quantum field theories for 3 manifolds with corners lecture notes in mathematics Posted By Louis L AmourMedia Publishing TEXT ID bea0 Online PDF Ebook Epub Library ebook kaufen isbn 3 5 versehen mit digitalem wasserzeichen drm frei. J. Ratcliffe, Foundations of Hyperbolic Manifolds, Springer. A text for n-dimensions. A. Marden, Outer Circles, Cambridge. An introduction to hy-perbolic 2- and 3-manifolds more or less parallel to our course. Soon to be replaced by the 2nd edition. K. Ohshika, Discrete Groups, AMS. An introduction to hyper-bolic group theory. theory. 0. Introduction In this paper we study fundamental groups of compact manifolds of positive isotropic curvature. We prove that the fundamental group of a compact Riemannian manifold with positive isotropic curvature of dimension ≥ 5 can not contain a surface group as a subgroup: Theorem Let M be a compact n-dimensional Riemannian man-.

## Group theory and three-dimensional manifolds by John R. Stallings Download PDF EPUB FB2

Buy Group Theory and Three-dimensional Manifolds (Mathematical Monograph, No. 4) on FREE SHIPPING on qualified orders Group Theory and Three-dimensional Manifolds (Mathematical Monograph, No. 4): Stallings, John R: : BooksCited by: Group theory and three-dimensional manifolds.

[John R Stallings] Home. WorldCat Home About WorldCat Help. Search. Search for Library Items Search for Lists Search for Book: All Authors / Contributors: John R Stallings. Find more information about: ISBN: OCLC Number: 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 Brand: Birkhäuser Basel. Hempel, Three-manifolds (main book on the course) Stillwell, Classical topology and combinatorial group theory (background material, and some 3-manifold theory) §1.

Introduction Deﬁnition. A (topological) n-manifold M is a Hausdorﬀ topological space with a countable basis of open sets, such that each point of M lies in an open set. This book provides a classification of all three-dimensional complex manifolds for which there exists a transitive action (by biholomorphic transformations) of a real Lie group.

This means two homogeneous complex manifolds are considered equivalent if they are isomorphic as complex manifolds. • A Haken manifold, M,is a compact, irreducible 3-manifold which con-tains a closed embedded surface with inﬁnite fundamental group that injects underthe map induced by inclusion into the fundamental group of manifolds include many important classes of 3-manifolds, and a great deal is.

[M, Y] W. Meeks and S-T Yau, Topology of three dimensional manifolds and the embedding problems in minimal surface theory, Ann. of Math. (), Zentralblatt MATH: Mathematical Reviews (MathSciNet): MR Digital Object Identifier: doi/ We present a survey of two-dimensional conformal field theory and show how the mathematical structures underlying conformal field theory can be used to construct invariants of links imbedded in a general class of three-dimensional manifolds.

After a general introduction, we discuss chiral algebras and their representation theory. Three-Dimensional Link Theory and Invariants of Plane Curve Singularities. (AM), Volume David Eisenbud and Walter D. Neumann. This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al.

of the theory of 3-manifolds. Group theory and three-dimensional manifolds, by John Stallings; Manifold wisdom: the Churches' ministry in the new age / Wesley Carr; Lectures on the automorphism groups of Kobayashi-hyperbolic manifolds / Alexander Isaev; The problem of truth / by H.

Wildon Carr. A decomposition of complete hyperbolic manifolds. Complete hyperbolic manifolds with bounded volume. Jørgensen’s Theorem. Chapter 6. Gromov’s invariant and the volume of a hyperbolic manifold Gromov’s invariant Gromov’s proof of Mostow’s Theorem Manifolds with Boundary 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 interplay of geometry, spectral theory and stochastics has a long and fruitful history, and is the driving force behind many developments in modern mathematics.

Bringing together contributions from a conference at the University of Potsdam, this volume focuses on global effects of local properties.

'This book is an attractive and comprehensive introduction to three-dimensional topology. The book is readable and inviting. Its many illustrations make it particularly accessible. This book promises to be a valuable text and reference for an exciting area of mathematics.' Price: $3-Manifolds. For 3-manifold theory there are several books: • W Thurston. Three-Dimensional Geometry and Topology. Princeton University Press, [$55] — A geometric introduction by the master.

Also useful for the geometry of surfaces. • A Hatcher. Basic Topology of 3-Manifolds. Unpublished notes available online at. Introduction Definition. A topological space X is a 3-manifold if it is a second-countable Hausdorff space and if every point in X has a neighbourhood that is homeomorphic to Euclidean 3-space.

Mathematical theory of 3-manifolds. The topological, piecewise-linear, and smooth categories are all equivalent in three dimensions, so little distinction is made in whether we are dealing with say. a coherent framework for relating the homotopy theory of manifolds to the algebraic theory of quadratic forms, unifying many of the previous results; 2.

a surgery obstruction theory for manifolds with arbitrary fundamental group, including the exact sequence for the set of manifold structures within a homotopy type, and many computations.

3-manifolds with torus boundary, including knot complements. Thus if two hyperbolic knot complements have isomorphic fundamental group, then they have exactly the same hyperbolic structure. Finally, Gordon and Luecke showed that two knot complements with the same fundamental group are equivalent [GL89] (up to mirror reﬂection).

You can write a book review and share your experiences. Other readers will always be interested in your opinion of the books you've read. Whether you've loved the book or not, if you give your honest and detailed thoughts then people will find new books that are right for them.

The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture. In Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology.

The Reviews:   Massey W S Algebraic topology, an introduction (Harcourt, Brace & World, New York) (this is a Russian translation of two books, one by) Stallings J R Group theory and three-dimensional manifolds (Yale Univ.

Press, New Haven) and one by. A familiar example is three-dimensional Euclidean space, with Cartesian coordinates (x,y,z). Thus our familiar three-dimensional space can be called the 3-manifold IR3. We can now give a formal deﬁnition of a smooth n-manifold, with a smooth atlas of charts, as 1.

A topological space S 2. An open cover {Ui}, which are known as patches. This is a continuation of the previous talk. (References: Stallings, Group theory and three-dimensional manifolds, Epstein, Ends, Topology of 3-manifolds and related topics, Peschke, The Theory of Ends, Calegari, Notes on 3-manifold topology.) 3/1/ —.

The theory of center manifold reduction is studied in this monograph in the context of (infinite-dimensional) Hamil- tonian and Lagrangian systems. The aim is to establish a "natural reduction method" for Lagrangian systems to their center manifolds.

Nonautonomous problems are considered as well. Example (An orientation-preserving crystallographic group). Here is one more three-dimensional example to illustrate the geometry of quotient spaces. Con sider the 3 families of lines in R3 of the form (t,n,m+1 2), (m+1 2,t,n) and (n,m+1 2,t) where nand mare integers and tis a real parameter.

They intersect a cube in the unit. In terms of bounding relations, one cannot analyze the topology of three-dimensional spaces closely enough to isolate the 3-sphere, while more general spaces cannot be isolated in terms of their groups.

The chapter explains how any unbounded manifold whose group is null has a rectilinear model in the space of inversion.

In this book, we present important recent results on the geometry and topology of 3-dimensional manifolds and orbifolds. Orbifolds are natural generalizations of manifolds, and can be roughly described as spaces which locally look like quo-tients of manifolds by ﬁnite group actions.

They were introduced by I. Satake. Topics. A manifold is a space whose topology, near any of its points, is the same as the topology near a point of a Euclidean space; however, its global structure may be ar examples of two-dimensional manifolds include the sphere, torus, and Klein bottle; this book concentrates on three-dimensional manifolds, and on two-dimensional surfaces within them.

Artin Presentation Theory, (AP Theory), is a new, direct infusion, via pure braid theory, of discrete group theory, (i.e., symmetry in its purest form), into the theory of {\it smooth} 4-manifolds.

The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic and differential topology, including the fundamental group, basic homology theory, transversality, and Poincaré duality on manifolds. Isometry group of hyperbolic manifolds CONTENTS vii Isometry group 66 Outer automorphism group 67 ogy and geometry that we will use in this book.

1. Di erential topology Di erentiable manifolds. A topological manifold of dimension Alexander as a counterexample to a natural three-dimensional general-ization of Jordan.

Fengfeng Ke, Valerie Shute, Kathleen M. Clark, and Gordon Erlebacher. Novem Mathematics Education.This book explains the following topics: the fundamental group, covering spaces, ordinary homology and cohomology in its singular, cellular, axiomatic, and represented versions, higher homotopy groups and the Hurewicz theorem, basic homotopy theory including fibrations and cofibrations, Poincare duality for manifolds and manifolds with boundary.