2 edition of **On the fundamental group of 3-gems and a planar class of 3-manifolds** found in the catalog.

On the fundamental group of 3-gems and a planar class of 3-manifolds

SoМЃstenes Lins

- 4 Want to read
- 18 Currently reading

Published
**1985** by Universidade Federal de Pernambuco, Centro de Ciências Exactas e da Natureza, Departamento de Matemática in Recife, Brasil .

Written in English

- Three-manifolds (Topology),
- Graph theory.

**Edition Notes**

Other titles | 3-gems and a "planar" class of 3-manifolds., Three-gems and a "planar" class of 3-manifolds. |

Statement | by Sóstenes Lins. |

Series | Notas e comunicações de matemática ;, no. 132 |

Classifications | |
---|---|

LC Classifications | QA1 .N863 no. 132, QA613.2 .N863 no. 132 |

The Physical Object | |

Pagination | 30 leaves : |

Number of Pages | 30 |

ID Numbers | |

Open Library | OL2333413M |

LC Control Number | 86222365 |

basic de nitions in group theory and 3-manifold topology. Then, we recall in Section 3 some of the key results in the study of 3-manifolds which appear time and again in the solutions to the decision problems. Finally in Section 4 we show that the ve aforementioned problems are indeed solvable for (most) 3-manifolds and their fundamental groups. The fundamental group and homology Special "core intuition" segments throughout the book briefly explain the basic intuition essential to understanding several topics. A generous number of figures and examples, many of which come from applications such as liquid crystals, space probe data, and computer graphics, are all available from the Price: $

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The planar 3-manifolds have other members beyond lens space" ©has fundamental group isomorphic to Z, + Q•• where Q. is the group fo quartemions; 0 has infinite fundamental group since this group has a quotient isomorphic to the free product of Zz by by: On the Fundamental Group of 3-Gems and a 'Planar' Class of 3-manifolds S6STENES LINS In this paper we associate a group YH to each bipartite 3-gem H.

By using the recent (Theorem I) graph-theoretical characterization of homeomorphisms among closed 3-manifolds due to Ferri and Gagliardi [6]this group is proven to be an invariant of IHI, the closed 3-manifold associated to H. This book grew out of a graduate course on 3-manifolds and is intended for a mathematically experienced audience that is new to low-dimensional topology.

The exposition begins with the definition of a manifold, explores possible additional structures on manifolds, discusses the classification of surfaces, introduces key foundational results for Cited by: 9.

In the final section we show how to construct a 3-gem ψ(G) from a planar graph G. By using theorems 2 and 3 we prove that the construction ψ has the following property: the number of spanning trees of G is equal to the order of the first homology group of |ψ(G)|.Author: Sóstenes Lins.

Prime 3 manifolds that are closed and orientable can be lumped broadly into three classes: Type I: ﬁnite fundamental group. For such a manifold M the universal cover Mfis simply-connected and closed, hence a homotopy sphere. All the known examples are spherical 3 manifolds, of the form M = S3/Γ for Γ a ﬁnite subgroup of SO(4) acting File Size: KB.

The key concept is the 3-gem, a special kind of edge-colored graph, which encodes the manifold via a ball complex. Passages between 3-gems and more standard presentations like Heegaard diagrams and surgery descriptions are provided. A catalogue of all closed orientable 3-manifolds induced by 3-gems up to 30 vertices is included.

Fundamental Group Homology Class Lens Space Torsion Subgroup Topological Classification These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm : Sóstenes L.

Lins, Vinicius G. Silva. The attractor of a 3-manifold M 3 is the set of all 3-gems which have a minimum number of vertices and induce M 3. A gem (graph-encoded manifold) is a special edge graph which encodes a ball complex whose underlying space is a manifold. Every 3-manifold is induced by a : Sóstenes Lins.

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) Stillwell, Classical topology and combinatorial group theory (background material, and some 3-manifold theory) §1.

Introduction Deﬁnition. The special class is formed by the duals of the {\em solvable gems}. On the fundamental group of 3-gems and a planar class of 3-manifolds. Framed link presentations of 3-manifolds by an {O. 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 On the fundamental group of 3-gems and a planar class of 3-manifolds book 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. On the fundamental group of closed 3-manifolds. I know that every finitely presented group can be realized as the fundamental group of a compact, connected, smooth manifold of dimension 4 (or higher). In dimension 2 there are strong restriction on the fundamental group of closed On the fundamental group of 3-gems and a planar class of 3-manifolds book.

There are two topological processes to join 3-manifolds to get a new one. The first is the connected sum of two manifolds and.

Choose embeddings and, remove the interior On the fundamental group of 3-gems and a planar class of 3-manifolds book and and glue and together along the boundaries On the fundamental group of 3-gems and a planar class of 3-manifolds book. The second uses incompressible surfaces.

Let be manifold and a surface. planar contact 3-manifolds, those supported by open book decompositions with genus zero pages, have been intensively studied to shed light on several aspects of 3-dimensional contact topology. Although all overtwisted contact 3-manifolds are known to be planar [18], there are some obstructions to planarity in dimension three (cf.

[18,32]).File Size: KB. AN INTRODUCTION TO 3-MANIFOLDS AND THEIR FUNDAMENTAL GROUPS 3. Contents Introduction 1 Caveat 1 Acknowledgment 2 1. Finitely presented groups and high dimensional manifolds 4 Finitely presented groups 4 Fundamental groups of high dimensional manifolds 4 2.

Surfaces and their fundamental groups 6 SYLVAIN MAILLOT John Hempel, 3-manifolds, Ann. of Math. Studies, vol. 86, Princeton University Press, Prince-ton, New Jersey, MR William.

of 3-orbifolds (and hence 3-manifolds) that have large fundamental group. Throughout this paper, an orbifold is allowed to have empty singular locus, and hence be a manifold.

If Ois a 3-orbifold and Lis a link in Odisjoint from the singular locus and nis a positive integer, then we denote by O(L,n) the orbifold. ON OPEN BOOKS FOR NONORIENTABLE 3-MANIFOLDS BURAK OZBAGCI show that the monodromy of Klassen’s genus two open book for P2 S1 is the Y-homeomorphism of Lickorish, which is also known as the cross- cap slide.

Similarly, we show that S2eS1 admits a genus two open book whose monodromy is the crosscap transposition. Moreover, we show that each of P2 S1. Mapping class group and fundamental group of a 3 manifold. If the 3 manifold is Haken, then the natural homomorphism from the mapping class group of this 3 manifold to the outer automorphism of its fundamental group is an isomorphism.

For each n-crystallization H, n ⩾ 2, we associate two sequences of groups ξkn(H), 0 ⩿ k ⩿ n − 1. These groups are proved to be invariant under the cry Cited by: 8. some known results concerning nilpotent groups of closed 3-manifolds to the more general class of compact 3-manifolds.

In the final section it is shown that each nonfinitely generated abelian group which occurs as a subgroup of the fundamental group of a 3-manifold is a subgroup of the additive group of rationals. (1) Introduction. 3-manifolds. This class of groups sits between the class of fundamental groups of surfaces, which for the most part are well understood, and the class of fundamen.

propose a strategy by which our contact invariant might be used to relate the fundamental group of a closed contact 3-manifold to properties of its Stein llings. Our construction is inspired by a reformulation of a similar invariant in the monopole Floer setting de ned by the authors in [1].

Introduction. Note that an irreducible 3-manifold with inﬁnite fundamental group is aspherical by the Sphere theorem and the Hurewicz theorem. For a space X with a homomorphism π 1(X) →π, usually an isomorphism, we will denote any continuous map that induces the homomorphism by c: X→Bπ.

Stable classiﬁcation of 4-manifolds with COAT. The fundamental group of this complex is also the fundamental group of a hyperbolic 3{manifold with boundary called a book of I{bundles [CS94].

(See also [HPW16] for more about these examples.) In contrast, by Theoremmost {hyperbolic groups in Care not fundamental groups of 3{manifolds.

Quasi-isometry classi cation. A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. sented group is the fundamental group of a closed k–dimensional man-ifold.

This is not the case for 3–manifolds, we will for example see that Z,Z/n,Z ⊕ Z/2 and Z3 are the only abelian groups which arise as fundamental groups of closed 3–manifolds. In the second section we recall the classiﬁcation of surfaces via their geometry and outline. In turn, our homology arguments in [Proposition 1] (cf.

[22, 31]) work the same for the induced positive factorizations of integral spinal open books, since the commutator elements in the mapping class description of a Lefschetz fibration over a non-planar base surface die in the first homology of the corresponding mapping class : R İnanç Baykur, Jeremy Van Horn-Morris.

Thanks for contributing an answer to Mathematics Stack Exchange. Please be sure to answer the question. Provide details and share your research. But avoid Asking for help, clarification, or responding to other answers.

Making statements based on opinion; back them up with references or personal experience. Use MathJax to format equations. The book will be accessible to graduate students in mathematics and theoretical physics familiar with some elementary algebraic topology, including the fundamental group, basic homology theory, and Poncaré duality on manifolds.

Enter your mobile number or email address below and we'll send you a link to download the free Kindle App. Cited by: Properties. A spherical 3-manifold has a finite fundamental group isomorphic to Γ itself. The elliptization conjecture, proved by Grigori Perelman, states that conversely all 3-manifolds with finite fundamental group are spherical manifolds.

The fundamental group is either cyclic, or is a central extension of a dihedral, tetrahedral, octahedral, or icosahedral group by a cyclic group of even. For certain small groups, it is easy (and desirable) to classify closed (and orientable if necessary) 3-manifolds with that group as their fundamental group.

(Essentially due to Waldhausen is that for "large" 3-manifold groups, indecomposable under free product, the 3-manifold is determined up to homeomorphism by its fundamental group, though.

Book Description: There is a sympathy of ideas among the fields of knot theory, infinite discrete group theory, and the topology of 3-manifolds. This book contains fifteen papers in which new results are proved in all three of these fields.

4 Nondestabilizable Planar Open Book Decompositions of S 3 In this section, we will prove Theorem To that end, let Σ n be a compact planar surface with (n +1)-boundary components, n ≥4, and ϕ n: Σ n → Σ n be a diffeomorphism obtained as the composition of right-handed Dehn twists along the curves shown in Figure by: 5.

In particular, Z cannot be the fundamental group of a closed manifold of Type III, which shows that S1 £ S2 is the only prime closed orientable 3-manifold with „ 1 infinite cyclic. Borel Conjecture: A closed n-manifold K(„,1) is determined up to homeomorphism by its fundamental group.

No counterexamples known in any Size: 57KB. This book offers a self-contained account of the 3-manifold invariants arising from the original Jones polynomial. These are the Witten-Reshetikhin-Turaev and the Turaev-Viro invariants.

Starting from the Kauffman bracket model for the Jones polynomial and the diagrammatic Temperley-Lieb algebra, higher-order polynomial invariants of links are constructed and combined to form the 3-manifold.

Algorithmic topology, or computational topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity theory. A primary concern of algorithmic topology, as its name suggests, is to develop efficient algorithms for solving problems that arise naturally in fields such as computational geometry, graphics.

THE FUNDAMENTAL GROUP OF S1-MANIFOLDS 3 Throughout, we shall choose an S1-invariant compatible pair, (J,g), of an almost complex structure and a Riemannian metric and we identify S1 with R/Z in the usual way to deﬁne the gradient of φ with respect to g.

This gradient is equal to Jξ M, where ξ M is the vector ﬁeld generating the action. 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., Free ebooks since the third homotopy group of some higher 35 dimensional knots by s.

lomonaco, jr. octahedral knot covers 47 by kenneth a. perko, jr. some knots spanned by more than one unknotted 51 surface of minimal genus by h. trotter groups and manifolds characterizing links 63 by wilbur whitten group theory hnn groups and groups with centre.

On the fundamental group of 3-gems and a pdf class of 3-manifolds, Lins, S., European Journal of Combinatorics 9 (4),Graphs of maps, Lins, S., arXiv:math/, Traversing trees and scheduling tasks for duplex corrugator machines, Lins, S., Pesquisa Operacional 9 Campo(s): Matemática, Computação.This method is useful download pdf study contact structures of 3-manifolds.

In this talk, we give a topological application of open book foliation techniques: We provide an estimation of the genus of essential surfaces in open books, in terms of its monodromy.

This provides a purely algebraic criterion for 3-manifolds to be irreducible or atroidal.Get this ebook a library! The geometric topology of 3-manifolds.

[R H Bing] -- This book belongs in both graduate and undergraduate libraries as a useful reference for students and researchers in topology. It is directed toward mathematicians interested in geometry who have had.