Normal Surfaces and Decision Problems in 3- Manifolds (Cbms Regional Conference Series in Mathematic)

by Hyam J. Rubinstein

Publisher: Amer Mathematical Society

Written in English
Published: Downloads: 51
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ID Numbers
Open LibraryOL11419632M
ISBN 100821805738
ISBN 109780821805732

The proof of these, and many other theorems in 3-manifold topology, depend on com- binatorial arguments; in the smooth category, such arguments depend on first putting a surface (or some other object) into general position; in the PL category, such argumentsFile Size: 1MB. Curvature Estimates for Constant Mean Curvature Surfaces in Three Manifolds by Sirong Zhang A dissertation submitted to the Johns Hopkins University in conformity with the requirements for the degree of ial normal bundle in a complete three manifold M. g is the Riemannian met-. Special cases of manifolds are the curves and the surfaces and these were quite well understood. B. Riemann was the first to note that the low dimensional ideas of his time were particular aspects of a higher dimensional world. The first chapter of this book introduces the reader to the concept of smooth manifold through. Summary. From the coauthor of Differential Geometry of Curves and Surfaces, this companion book presents the extension of differential geometry from curves and surfaces to manifolds in provides a broad introduction to the field of differentiable and Riemannian manifolds, tying together the classical and modern formulations.

Minimal surfaces and particles in 3-manifolds Kirill Krasnov ∗and Jean-Marc Schlenker † January (v3) Abstract We consider 3-dimensional anti-de Sitter manifolds with conical singularities along time-like lines, which is what in the physics literature is known as manifolds with particles. We show that the space of such. () Benders Decomposition and Normal Boundary Intersection Method for Multiobjective Decision Making Framework for an Electricity Retailer in Energy Markets. IEEE Systems Journal , () A model-based approach to multi-objective by: Let Mg denote the moduli space of Riemann surfaces. The group Modg acts properly discon- tinuously on the Teichmuller¨ space Teichg of marked, genus g Riemann surfaces. Since Teichg is contractible it follows that Mg is a K(Modg,1) space, i.e. it is homotopy equivalent to the spaces in (1). From these considerations it morally follows that, for any topological space B, we have the. restricts attention to sub manifolds of Euclidean space while the latter studies manifolds equipped with a Riemannian metric. The extrinsic theory is more accessible because we can visualize curves and surfaces in R 3, but some topics can best be handled with the intrinsic Size: KB.

Haken hyperbolic 3-manifolds: Wise’s Theorem 48 Quasi-Fuchsian surface subgroups: the work of Kahn and Markovic 50 Agol’s Theorem 50 3-manifolds with non-trivial JSJ decomposition 51 3-manifolds with more general boundary 52 Summary of previous research on the virtual conjectures 54 6. k 3 3 gold badges 62 62 silver badges bronze badges $\endgroup$ $\begingroup$ I can see just by homology considerations that the Euler class distinguishes the boundaries of the orientable disk bundles over orientable surfaces. 1 The surgery classification of manifolds 1 2 Manifolds 13 Differentiable manifolds 13 Surgery 14 Morse theory 17 Handles 20 3 Homotopy and homology 26 Homotopy 26 Homology 29 4 Poincar´e duality 42 Poincar´e duality 42 The homotopy and homology effects of surgery 47 Surfaces 53 Rings with involution 8 2. BACKGROUND Proof. By a homothetic rescaling we may take s= 1. Now x a point x2 B 2 \. As is smooth and x;1 is compact there is a uniform >0 (in principal depending on) so that for each point y2 x;1 so that y; can be written as the graph of a File Size: KB.

Normal Surfaces and Decision Problems in 3- Manifolds (Cbms Regional Conference Series in Mathematic) by Hyam J. Rubinstein Download PDF EPUB FB2

Request PDF | On May 1,S.V. Matveev and others published Normal surfaces in 3-manifold | Find, read and cite all the research you need on ResearchGate.

This is a personal view of some problems on minimal surfaces, Ricci flow, polyhedral geometric structures, Haken 4-manifolds, contact structures and Heegaard splittings, singular incompressible Author: Hyam Rubinstein. Finding non-orientable surfaces in 3-manifolds Benjamin A.

Burtony Arnaud de Mesmayz Uli Wagnerx September 2, Abstract We investigate the complexity of nding an embedded non-orientable surface of Euler genus gin a triangulated 3-manifold. This problem occurs both as a natural question inAuthor: Benjamin A. Burton, Normal Surfaces and Decision Problems in 3- Manifolds book de Mesmay, Uli Wagner.

Algorithmic Topology and Classification of 3-Manifolds serves as a standard reference for algorithmic 3-dimensional topology for both graduate students and researchers. Release Immersed normal surfaces and decision problems for 3-manifolds. 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. Rubinstein, J. Polyhedral minimal surfaces, Heegaard splittings and decision problems for 3-dimensional manifolds / by J.H.

Rubinstein Dept. of Mathematics, University Melbourne [Parkville, Vic.] Australian/Harvard Citation. Normal surfaces 11 6. The matching equations and fundamental surfaces 13 However, Matveev’s book [50] is also an excellent resource, particularly for the material on normal surfaces in Sections 5, 6 and ural to ask whether there are any decision problems about 3-manifolds for which we can pin down their complexity.

Perhaps Author: Marc Lackenby. Normal surface theory, a tool to represent surfaces in a triangulated 3-manifold combinatorially, is ubiquitous in computational 3-manifold theory. In this paper, we investigate a relaxed notion of normal surfaces where we remove the quadrilateral conditions.

This yields normal surfaces that are no longer embedded. We prove that it is NP-hard to decide whether such a surface is. tive of normal surfaces. We begin with an overview of manifolds before exploring 3-manifolds in more depth.

The goal of section 2 and section 3 is to provide the language necessary to properly discuss the theory of normal surfaces and 3-manifold algorithms. The section 4 fully develops normal surface theory. This is the largest section and repre. Abstract: This carefully written book is an introduction to the beautiful ideas and results of differential geometry.

The first half covers the geometry of curves and surfaces, which provide much of the motivation and intuition for the general theory. dimensional open ball. We will be focusing on 3-manifolds much the same way we looked at 2-manifolds (surfaces). A basic example of a 3-Manifold: R3 is a 3-manifold because every point in R3 is contained in an open ball in R3.

Our study of 3-Manifolds will bene t greatly by making sure we have a strong standing in surfaces. Abstract. We survey the status of some decision problems for 3-mani-folds and their fundamental groups.

This includes the classical decision problems for nitely presented groups (Word Problem, Conjugacy Prob-lem, Isomorphism Problem), and also the Homeomorphism Problem for 3-manifolds and the Membership Problem for 3-manifold groups. Introduction.

The set of all normal surfaces in a 3-manifold is a partial monoid under addition with a minimal generating set of fundamental surfaces. The available algorithm for finding the system of fundamental surfaces is of a theoretical nature and admits no implementation in by: 2.

Tu's book is definitely a great book to read for someone who doesn't know the first thing about manifolds. I have sampled many books on manifold theory and Tu's seems the friendliest.

The most illuminating aspect of it, for me at least, is the fact that it presents the basics of differential and integral calculus on $\mathbb{R}^n$ in a.

tive of normal surfaces. We begin with an overview of manifolds before exploring 3-manifolds in more depth. The goal ofsection 2 andsection 3 is to provide the language necessary to properly discuss the theory of normal surfaces and 3-manifold algorithms. Thesection 4 fully develops normal surface theory.

This is the largest section and repre-Author: Josh D Hews. AN INTRODUCTION TO 3-MANIFOLDS 5 In the study of surfaces it is helpful to take a geometric point of view.

In particular, note that if a closed surface Σ admits a Riemannian metric of area A and constant curvature K, then it follows from the Gauss–Bonnet theorem, that K A = 2πχ(Σ).

The second part, chapters 10 is an attempt to remedy the notorious absence in the original book of any treatment of surfaces in three-space, an omission all the more unforgivable in that surfaces are some of the most common geometrical objects, not only in mathematics but in many branches of by: The Virtually Fibred Conjecture, and related problems.

For a weaker definition of 3-manifold topology, I think the Andrews-Curtis conjecture is a key problem. Also, anything which relates to the classification of non-simply-connected topological 4-manifolds, for instance problems related to knot and link concordance.

The Classification Problem for 3-Manifolds 1. Canonical decomposition into simpler pieces. Program from ca. Explicit classification of special types of pieces.

Generic pieces are hyperbolic manifolds. Will focus on the more topological aspects, File Size: 57KB. theorem, will be given. Many problems about 3–manifolds are solved using the concepts of incompressible surfaces and hierarchies due to Haken, and practical algorithms for decision problems use the theory of normal surfaces.

The course will end with a weak geometrisation theorem for Haken 3–manifolds—focussing not onFile Size: 93KB. 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. The proofs use minimal (or maximal, or CMC) surfaces, along with some results of Mess on AdS manifolds, which are recovered here in a different way, using differential-geometric methods and a result of Labourie on some mappings between hyperbolic surfaces, that allows an extension to by: Dr.

William "Bus" H. Jaco (born J in Grafton, West Virginia) is an American mathematician, who currently resides in Stillwater, is known for his role in the Jaco–Shalen–Johannson decomposition theorem and is currently Regents Professor and Grayce B.

Kerr Chair at Oklahoma State University as well as Executive Director of the Initiative for Born: J (age 79), Grafton, West. IMMERSIONS OF SURFACES IN 3-MANIFOLDS respondence in the other direction, when it is 1-to-1, and a homotopy inverse on one component when it is 2-to Now let E = f M.

Then the differential of fo gives a splitting of E as T F EE)N, where N is Cited by: 5. Decision problems in the space of Dehn fillings: essential surfaces.

In this section we consider the existence of certain interesting surfaces in Dehn fillings of a knot-manifold X. Recall that a surface S properly embedded in a 3-manifold M is compressible if there is an embedded disk D⊂M so that ∂D⊂S is a non-trivial curve in by: TOPOLOGICAL INDEX THEORY FOR SURFACES IN 3-MANIFOLDS 5 contains an incompressible surface.

Critical surfaces were also instru-mental in the author’s proof of a conjecture of C. Gordon [Bac08]. Definition H is critical if the compressions for H can be parti-tioned into sets C0 and C1 such that: (1) For each i =0,1 there is at least one.

The Geometry and Topology of Three-Manifolds Electronic version - March Thurston — The Geometry and Topology of 3-Manifolds iii. Contents Introduction iii Chapter 1.

Geometry and three-manifolds 1 Horospheres. 38 Hyperbolic surfaces obtained from ideal triangles. 40 Hyperbolic manifolds obtained by gluing File Size: 1MB. The necessary prerequisite is a good knowledge of the calculus with several variables, linear algebra and some elementary point-set tried to address several issues.

The Language; 2. The Problems; 3. The Methods; 4. The ically, the problems came first, then came the methods and the language while the answers came by: a 3-manifold bounds a singular disk in the manifold, then it bounds an embedded disk.

His proof employed an ingenious technique, a “tower construction,” that enabled him to fashion two more important tools, the loop theorem and the sphere theorem. The study of surfaces in 3-manifolds would advance immeasurably. THE GEOMETRY OF SURFACES AND 3-MANIFOLDS ROBERT YOUNG Note: Most of the illustrations in these notes are omitted.

Please draw your own. Surfaces A surface is a space where every point has a neighborhood which is (topologically) an open disc. Example The plane is a surface; every point has a neighborhood which is a disc. Example. THE GEOMETRY OF SURFACES AND 3-MANIFOLDS ROBERT YOUNG Note: Most of the illustrations in these notes are omitted.

Please draw your own! 4. A 3-manifold bestiary How does all of this generalize to three-dimensional manifolds? In gen-eral, the picture is a lot more complicated, because 3-manifolds are a lot more Size: 83KB.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.Lecture 3: 2-Manifolds Surface Classification, Polygonal Scheme, Euler-Characteristic Scribed by: Xiaoyin Ge 1 Surface Classification 2-manifolds, often referred to as surfaces, are of special interest, as they appear most often in real life, especially in graphics.

In this class and next class, we will focus on 2-manifolds, talking about how toFile Size: 76KB.