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1 edition of Torsions of 3-dimensional Manifolds found in the catalog.

Torsions of 3-dimensional Manifolds

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Published by Birkhäuser Basel, Imprint, Birkhäuser in Basel .
Written in English

    Subjects:
  • Mathematics,
  • Cell aggregation,
  • Global analysis,
  • Topology

  • About the Edition

    The book is concerned with one of the most interesting and important topological invariants of 3-dimensional manifolds based on an original idea of Kurt Reidemeister (1935). This invariant, called the maximal abelian torsion, was introduced by the author in 1976. The purpose of the book is to give a systematic exposition of the theory of maximal abelian torsions of 3-manifolds. Apart from publication in scientific journals, many results are recent and appear here for the first time. Topological properties of the torsion are the main focus. This includes a detailed description of relations between the torsion and the Alexander-Fox invariants of the fundamental group. The torsion is shown to be related to the cohomology ring of the manifold and to the linking form. The reader will also find a definition of the torsion norm on the 2-homology of a 3-manifold, and a comparison with the classical Thurston norm. A surgery formula for the torsion is provided which allows to compute it explicitly from a surgery presentation of the manifold. As a special case, this gives a surgery formula for the Alexander polynomial of 3-manifolds. Treated in detail are a number of relevant notions including homology orientations, Euler structures, and Spinc structures on 3-manifolds. Relations between the torsion and the Seiberg-Witten invariants in dimension 3 are briefly discussed. Students and researchers with basic background in algebraic topology and low-dimensional topology will benefit from this monograph. Previous knowledge of the theory of torsions is not required. Numerous exercises and historical remarks as well as a collection of open problems complete the exposition.

    Edition Notes

    Statementby Vladimir Turaev
    SeriesProgress in Mathematics -- 208, Progress in Mathematics -- 208.
    Classifications
    LC ClassificationsQA614-614.97
    The Physical Object
    Format[electronic resource] /
    Pagination1 online resource (X, 196 pages).
    Number of Pages196
    ID Numbers
    Open LibraryOL27092391M
    ISBN 103034879997
    ISBN 109783034879996
    OCLC/WorldCa840290306

    C2 codimension one foliation of a compact 3-dimensional manifold with nite fundamental group has a compact leaf. The basic ideas leading to Novikov’s Theorem are surveyed here.1 1 Introduction Intuitively, a foliation is a partition of a manifold M into submanifolds Aof the same dimension that stack up locally like the pages of a book. THE CLASSICAL PLATEAU PROBLEM AND THE TOPOLOGY OF THREE-DIMENSIONAL MANIFOLDS THE EMBEDDING OF THE SOLUTION GIVEN BY DOUGLAS-MORREY AND AN ANALYTIC PROOF OF DEHN’S LEMMA WILLIAM H. MEEKS III? and SHING-TUNG YAUS (Received 16 July ) NRODUCTION LET y be a rectifiable Jordan curve in three-dimensional euclidean . Visualizing 3-Dimensional Manifolds Dugan J. Hammock Dept. of Mathematics, University of Massachusetts Lederle Graduate Research Tower, Amherst, MA , USA [email protected] Abstract Given a parametrized 3-dimensional manifold sitting in 4-dimensional space, we wish to visualize it by looking at. of a 3-dimensional manifold in the sense that it completely determines such a manifold, but, unfortunately, a 3-dimensional manifold gives rise to an infinity of diagrams. The problem of classifying manifolds is thus transferred to the problem of classifying diagrams.

      This book is an introduction to combinatorial torsions of cellular spa ces and manifolds with special emphasis on torsions of 3-dimensional m anifolds. The first two chapters cover algebraic foundations of the th eory of torsions and various topological constructions Brand: Cold Spring Press.


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Torsions of 3-dimensional Manifolds by Vladimir Turaev Download PDF EPUB FB2

Torsions of 3-Dimensional Manifolds (Progress in Mathematics) nd Edition by Vladimir Turaev (Author) › Visit Amazon's Vladimir Turaev Page.

Find all the books, read about the author, and more. See search results for this author. Are you an author. Cited by: : Torsions of 3-dimensional Manifolds (Progress in Mathematics) (): V.

Turaev: Books. Three-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc. This book belongs to the second domain. We shall study an invariant called the maximal abelian torsion and denoted T.

It isBrand: Birkhäuser Basel. Three-dimensional topology includes two vast domains: the study of geometric structures on 3-manifolds and the study of topological invariants of 3-manifolds, knots, etc.

This book belongs to the second domain. We shall study an invariant called the maximal abelian torsion and denoted T. Torsions of 3-dimensional manifolds. [Vladimir Georgievich Turaev] "This is an excellent exposition about abelian Reidemeister torsions for three-manifolds."-Zentralblatt Math"The present monograph covers in great detail the work of the author spanning almost three Read more Book\/a>, schema:CreativeWork\/a>.

Get this from a library. Torsions of 3-dimensional Manifolds. [Vladimir Turaev] -- The book is concerned with one of the most interesting and important topological invariants of 3-dimensional manifolds based on an original idea of Kurt Reidemeister ().

This invariant, called. This is a survey on Reidemeister torsion for hyperbolic three-manifolds of finite volume. Torsions are viewed as topological invariants and also as functions on the variety of representations in Author: Gwenael Massuyeau.

In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. A 3-manifold can be thought of as a possible shape of the as a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer.

This is made more precise in the definition below. Cite this chapter as: Turaev V. () Euler Structures on 3-manifolds. In: Torsions of 3-dimensional Manifolds. Progress in Mathematics, vol Author: Vladimir Turaev.

The main problem in the topology of three-dimensional manifolds is that of their classification. A three-dimensional manifold is said to be simple if implies that exactly one of the manifolds, is a sphere.

Every compact three-dimensional manifold decomposes into a connected sum of a finite number of simple three-dimensional manifolds. The aim of the lectures is to survey the theory of torsions of 3-dimensional manifolds.

The torsions were introduced by Kurt Reidemeister in to give a topological classification of lens spaces. Recent interest in torsions is due to their connections with the Seiberg-Witten invariants of 4-manifolds and the Floer-type homology of 3-manifolds.

In Section 2, we recall the definitions of Reidemeister torsions and twisted Alexander invariants and then fix the notation.

Section 3 is devoted to explaining how to obtain the n-dimensional. The Mathematics of Three-dimensional Manifolds Topological study of these higher-dimensional analogues of a surface suggests the universe may be as convoluted as a tangled loop of string.

It now appears most of the manifolds can be analyzed geometrically by William P. Thurston and Jeffrey R. Weeks Thousands of years ago many peo­File Size: KB. Since Reidemeister torsions of rational homology 3-spheres are elements in cyclotomic fields, we need algebraic number theoretical studies.

Recently P Ozsvath and Z Szabo defined the Heegaard Floer homology which is a powerful invariant to study 3-manifolds. It induces the Reidemeister-Turaev torsion. We also explain it here. Contents: Preface. nity to present a few aspects of 3-dimensional topology. We have focussed on closed oriented 3-manifolds to simplify the exposition, although most of the material extends to compact 3-manifolds with toroidal boundary (which include link complements).

Besides. Algebraic Torsion in Higher-Dimensional Contact Manifolds 3 Zusammenfassung Wir konstruieren Beispiele von Kontaktmannigfaltigkeiten in jeder unge-raden Dimension, welche endliche nicht-triviale algebraische Torsion (im Sin-ne von [LW11]) aufweisen, somit stra sind und keine starke symplektische F.

The Geometry and Topology of Three-Manifolds Electronic version - March chapters have not yet appeared in book form. Please send corrections to Silvio Levy at [email protected] Thurston — The Geometry and Topology of 3-Manifolds iii.

Contents Introduction iii File Size: 1MB. Offers an Introduction to combinatorial torsions of cellular spaces and manifolds with emphasis on torsions of 3-dimensional manifolds.

This book describes the results of G Meng, C H Taubes and the author on the connections between the refined torsions and the Seiberg-Witten invariant of 3-manifolds.

Book Notices Book Notices JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol.No. 2, pp. –, November () Turaev, V., Torsions of 3-Dimensional Manifolds, Birkhauser Verlag, Basel, Switzerland, ( pages).

Contents. Introduction. Generalities on torsions. Torsion versus the Alex- ander-Fox invariants. Vladimir Turaev (auth.): free download. Ebooks library. On-line books store on Z-Library | B–OK. Download books for free. Find books. INTRODUCTION TO 3-MANIFOLDS 5 The 3-torus is a 3-manifold constructed from a cube in R3.

Let each face be identi ed with its opposite face by a translation (without twisting). You can imagine this as a direct extension from the 2-torus we are comfortable with. If you were to sit inside of a 3-torus. Chapter 1) Geometry and three-manifolds (with front page, introduction, and table of contents), i–vii, 1–7 PDF PS ZIP TGZ Chapter 2) Elliptic and hyperbolic geometry, 9–26 PDF PS ZIP TGZ Chapter 3) Geometric structures on manifolds, 27–43 PDF PS ZIP TGZ.

Topology and Geometry of 2 and 3 dimensional manifolds Chris John May 3, Supervised by Dr. Tejas Kalelkar 1 Introduction In this project I started with studying the classi cation of Surface and then I started studying some preliminary topics in 3 dimensional manifolds.

2 Surfaces De nition Three-Dimensional Manifolds Michaelmas Term Prerequisites Basic general topology (eg. compactness, quotient topology) Basic algebraic topology (homotopy, fundamental group, homology) Relevant books Armstrong, Basic Topology (background material on algebraic topology) Hempel, Three-manifolds (main book on the course).

K2 and Diffeomorphisms of Two and Three Dimensional Manifolds Assume M is oriented and suppose / £ V(x) is a diffeomorphism of the triple (M;N3Nf) which preserves orientation. Let / denote The / considered as a diffeomorphism of the triple (M;N'3N). conjugation ~": F + F induces an involution defined by {x,y} = {x3y}.Cited by: 3.

4 Thus, we have proved the following Theorem F i be a connected, compact, closed, smooth manifold of dimension n. Then F i = C UKn,Cn IKn-1 =Æ, where K i is an i–dimensional cell and D i–1is a union of some finite number of (i–1)–simplexes of the triangulation.

3°.We consider the initial simplexn d 0 of the triangulation and its center k. This book is an introduction to combinatorial torsions of cellular spa ces and manifolds with special emphasis on torsions of 3-dimensional m anifolds.

The first two chapters cover algebraic foundations of the th eory of torsions and various topological constructions of torsions due to K. Reidemeister, J.H.C.

Whitehead, J. Milnor and the : Vladimir Turaev. Introduction to Combinatorial Torsions by Vladimir Turaev,available at Book Depository with free delivery : Vladimir Turaev. TY - JOUR AU - Rumin, Michel AU - Seshadri, Neil TI - Analytic torsions on contact manifolds JO - Annales de l’institut Fourier PY - PB - Association des Annales de l’institut Fourier VL - 62 IS - 2 SP - EP - AB - We propose a definition for analytic torsion of the contact complex on contact manifolds.

We show it coincides with Ray–Singer torsion on any $3$-dimensional CR Cited by:   Lecture 4: Differentiable Manifolds (International Winter School on Gravity and Light ) - Duration: The WE-Heraeus International Winter School on Gravity and Li views.

If all critical manifolds are nondegenerate in this sense we say that E is a Morse-Bott function. Let ΛaM be the set E−1([0,a]) ⊆ ΛM.

If N is the only critical submanifold of energy a, one can use the gradient ow to show that there is a homotopy equiva-lence Λa+ M ’ Λa− M. Discover Book Depository's huge selection of V G Turaev books online. Free delivery worldwide on over 20 million titles.

In the post-war years, the theory of 3-dimensional manifolds has developed tremendously. On the one hand, Bing and Moise have proved that 3-manifolds can be triangulated, and that the Hauptvermutung (that any two triangulations of the same space are combinatorially equivalent) is true for 3-manifolds.

Quantum invariants of knots and 3-manifolds. De Gruyter. Vladimir G. Turaev. Year: Torsions of 3-dimensional Manifolds. Birkhäuser Basel. Vladimir Turaev (auth.) Year: A search query can be a title of the book, a name of the author, ISBN or anything else. 3-dimensional geometries and there are eight of them.

See §4 and §5. It is easy to see from the classification of these geometries that many closed 3-manifolds do not possess a geometric structure. For example, no connected sum of closed manifolds, excep3 #t File Size: 8MB. $\begingroup$ I recall Turaev works out the details of lens spaces in his book Torsions of 3-Dimensional Manifolds beginning with a cell decomposition and accompanying explicit bases for homology.

It was very clarifying (but not, I fear, so clarifying that I remember enough to write an answer off the top of my head). $\endgroup$ – Neal Nov We propose a definition for analytic torsion of the contact complex on contact manifolds.

We show it coincides with Ray-Singer torsion on any 3-dimensional CR Seifert manifold equipped with a unitary representation. In this particular case we compute it and relate it to dynamical properties of the Reeb flow. 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.5/5(1).

Three-Dimensional Parametric Design Of Manifold Blocks. We must obey the rule of the manifold characteristics before design a manifold block: 1. Small size, light weight, compact structure 2.

No leakage, the use of threaded mounting 3. Easy installation and maintenance 4. To minimize the original pipe installation 5. Optimized system design.

THREE-DIMENSIONAL MANIFOLD. We will only deal here with the topological aspect of this notion. A (topological) 3-dimensional manifold (or space), or 3-manifold, is a topological space locally homeomorphic to the 3-dimensional Euclidian space or to the half-space (i.e.

for which every point has a neighborhood homeomorphic to or); it is a 3-dimensional topological manifold. [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/Topology and Geometry of Three-Dimensional Manifolds Stephan Tillmann (Version ) Ja mach nur einen Plan, [Make yourself a plan,] sei nur ein grosses Licht! [be a clever chap!] Und mach dann noch ’nen zweiten Plan, [And then make another plan,] gehn tun sie beide nicht.

[neither of them works.]File Size: 93KB.In mathematics, Reidemeister torsion (or R-torsion, or Reidemeister–Franz torsion) is a topological invariant of manifolds introduced by Kurt Reidemeister (Reidemeister ) for 3-manifolds and generalized to higher dimensions by Wolfgang Franz () and Georges de Rham ().

Analytic torsion (or Ray–Singer torsion) is an invariant of Riemannian manifolds defined by Daniel B. Ray and Isadore M.