Surfaces In 4 Space

Author : Scott Carter,Seiichi Kamada,Masahico Saito
Publisher : Springer Science & Business Media
Page : 220 pages
File Size : 51,8 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662101629

Get Book

Surfaces in 4-Space by Scott Carter,Seiichi Kamada,Masahico Saito Pdf

Surfaces in 4-Space, written by leading specialists in the field, discusses knotted surfaces in 4-dimensional space and surveys many of the known results in the area. Results on knotted surface diagrams, constructions of knotted surfaces, classically defined invariants, and new invariants defined via quandle homology theory are presented. The last chapter comprises many recent results, and techniques for computation are presented. New tables of quandles with a few elements and the homology groups thereof are included. This book contains many new illustrations of knotted surface diagrams. The reader of the book will become intimately aware of the subtleties in going from the classical case of knotted circles in 3-space to this higher dimensional case. As a survey, the book is a guide book to the extensive literature on knotted surfaces and will become a useful reference for graduate students and researchers in mathematics and physics.

Author : J. Scott Carter
Publisher : World Scientific
Page : 344 pages
File Size : 55,5 Mb
Release : 1995
Category : Science
ISBN : 9810220669

Get Book

How Surfaces Intersect in Space by J. Scott Carter Pdf

This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. It will be of value to anyone who wants to understand the subject by way of examples. Undergraduates, beginning graduate students, and non-professionals will profit from reading the book and from just looking at the pictures.

Author : Richard Evan Schwartz
Publisher : American Mathematical Soc.
Page : 330 pages
File Size : 48,7 Mb
Release : 2011
Category : Hypersurfaces
ISBN : 9780821853689

Get Book

Mostly Surfaces by Richard Evan Schwartz Pdf

The goal of the book is to present a tapestry of ideas from various areas of mathematics in a clear and rigorous yet informal and friendly way. Prerequisites include undergraduate courses in real analysis and in linear algebra, and some knowledge of complex analysis. --from publisher description.

Author : J. Scott Carter,Masahico Saito
Publisher : American Mathematical Society
Page : 273 pages
File Size : 52,6 Mb
Release : 2023-12-06
Category : Mathematics
ISBN : 9781470476335

Get Book

Knotted Surfaces and Their Diagrams by J. Scott Carter,Masahico Saito Pdf

In this book the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in 3-dimensional space. In the first chapter knotted surface diagrams are defined and exemplified; these are generic surfaces in 3-space with crossing information given. The diagrams are further enhanced to give alternative descriptions. A knotted surface can be described as a movie, as a kind of labeled planar graph, or as a sequence of words in which successive words are related by grammatical changes. In the second chapter, the theory of Reidemeister moves is developed in the various contexts. The authors show how to unknot intricate examples using these moves. The third chapter reviews the braid theory of knotted surfaces. Examples of the Alexander isotopy are given, and the braid movie moves are presented. In the fourth chapter, properties of the projections of knotted surfaces are studied. Oriented surfaces in 4-space are shown to have planar projections without cusps and without branch points. Signs of triple points are studied. Applications of triple-point smoothing that include proofs of triple-point formulas and a proof of Whitney's congruence on normal Euler classes are presented. The fifth chapter indicates how to obtain presentations for the fundamental group and the Alexander modules. Key examples are worked in detail. The Seifert algorithm for knotted surfaces is presented and exemplified. The sixth chapter relates knotted surfaces and diagrammatic techniques to 2-categories. Solutions to the Zamolodchikov equations that are diagrammatically obtained are presented. The book contains over 200 illustrations that illuminate the text. Examples are worked out in detail, and readers have the opportunity to learn first-hand a series of remarkable geometric techniques.

Author : Charles Livingston
Publisher : Unknown
Page : 106 pages
File Size : 53,5 Mb
Release : 1980
Category : Electronic
ISBN : UCAL:C2939290

Get Book

The Knotting of Surfaces in 4-space by Charles Livingston Pdf

Author : Benson Farb,Richard Hain,Eduard Looijenga
Publisher : American Mathematical Soc.
Page : 371 pages
File Size : 47,5 Mb
Release : 2013-08-16
Category : Mathematics
ISBN : 9780821898871

Get Book

Moduli Spaces of Riemann Surfaces by Benson Farb,Richard Hain,Eduard Looijenga Pdf

Mapping class groups and moduli spaces of Riemann surfaces were the topics of the Graduate Summer School at the 2011 IAS/Park City Mathematics Institute. This book presents the nine different lecture series comprising the summer school, covering a selection of topics of current interest. The introductory courses treat mapping class groups and Teichmüller theory. The more advanced courses cover intersection theory on moduli spaces, the dynamics of polygonal billiards and moduli spaces, the stable cohomology of mapping class groups, the structure of Torelli groups, and arithmetic mapping class groups. The courses consist of a set of intensive short lectures offered by leaders in the field, designed to introduce students to exciting, current research in mathematics. These lectures do not duplicate standard courses available elsewhere. The book should be a valuable resource for graduate students and researchers interested in the topology, geometry and dynamics of moduli spaces of Riemann surfaces and related topics. Titles in this series are co-published with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.

Author : Áurea Casinhas Quintino
Publisher : Cambridge University Press
Page : 261 pages
File Size : 52,9 Mb
Release : 2021-06-10
Category : Mathematics
ISBN : 9781108794428

Get Book

Constrained Willmore Surfaces by Áurea Casinhas Quintino Pdf

From Bäcklund to Darboux: a comprehensive journey through the transformation theory of constrained Willmore surfaces, with applications to constant mean curvature surfaces.

Author : W.H. III Meeks,A. Ros,H. Rosenberg
Publisher : Springer
Page : 124 pages
File Size : 52,8 Mb
Release : 2004-10-11
Category : Mathematics
ISBN : 9783540456094

Get Book

The Global Theory of Minimal Surfaces in Flat Spaces by W.H. III Meeks,A. Ros,H. Rosenberg Pdf

In the second half of the twentieth century the global theory of minimal surface in flat space had an unexpected and rapid blossoming. Some of the classical problems were solved and new classes of minimal surfaces found. Minimal surfaces are now studied from several different viewpoints using methods and techniques from analysis (real and complex), topology and geometry. In this lecture course, Meeks, Ros and Rosenberg, three of the main architects of the modern edifice, present some of the more recent methods and developments of the theory. The topics include moduli, asymptotic geometry and surfaces of constant mean curvature in the hyperbolic space.

Author : Taha Sochi
Publisher : Taha Sochi
Page : 252 pages
File Size : 54,6 Mb
Release : 2022-09-14
Category : Mathematics
ISBN : 8210379456XXX

Get Book

Introduction to Differential Geometry of Space Curves and Surfaces by Taha Sochi Pdf

This book is about differential geometry of space curves and surfaces. The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with an index, extensive sets of exercises and many cross references, which are hyperlinked for the ebook users, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

Author : Sebastián Montiel,Antonio Ros
Publisher : American Mathematical Soc.
Page : 395 pages
File Size : 46,7 Mb
Release : 2009
Category : Curves on surfaces
ISBN : 9780821847633

Get Book

Curves and Surfaces by Sebastián Montiel,Antonio Ros Pdf

Offers a focused point of view on the differential geometry of curves and surfaces. This monograph treats the Gauss - Bonnet theorem and discusses the Euler characteristic. It also covers Alexandrov's theorem on embedded compact surfaces in R3 with constant mean curvature.

Author : Francis E. Burstall,Dirk Ferus,Katrin Leschke,Franz Pedit,Ulrich Pinkall
Publisher : Springer
Page : 96 pages
File Size : 50,5 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540453017

Get Book

Conformal Geometry of Surfaces in S4 and Quaternions by Francis E. Burstall,Dirk Ferus,Katrin Leschke,Franz Pedit,Ulrich Pinkall Pdf

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Author : Shoshichi Kobayashi
Publisher : Springer Nature
Page : 192 pages
File Size : 49,5 Mb
Release : 2019-11-13
Category : Mathematics
ISBN : 9789811517396

Get Book

Differential Geometry of Curves and Surfaces by Shoshichi Kobayashi Pdf

This book is a posthumous publication of a classic by Prof. Shoshichi Kobayashi, who taught at U.C. Berkeley for 50 years, recently translated by Eriko Shinozaki Nagumo and Makiko Sumi Tanaka. There are five chapters: 1. Plane Curves and Space Curves; 2. Local Theory of Surfaces in Space; 3. Geometry of Surfaces; 4. Gauss–Bonnet Theorem; and 5. Minimal Surfaces. Chapter 1 discusses local and global properties of planar curves and curves in space. Chapter 2 deals with local properties of surfaces in 3-dimensional Euclidean space. Two types of curvatures — the Gaussian curvature K and the mean curvature H —are introduced. The method of the moving frames, a standard technique in differential geometry, is introduced in the context of a surface in 3-dimensional Euclidean space. In Chapter 3, the Riemannian metric on a surface is introduced and properties determined only by the first fundamental form are discussed. The concept of a geodesic introduced in Chapter 2 is extensively discussed, and several examples of geodesics are presented with illustrations. Chapter 4 starts with a simple and elegant proof of Stokes’ theorem for a domain. Then the Gauss–Bonnet theorem, the major topic of this book, is discussed at great length. The theorem is a most beautiful and deep result in differential geometry. It yields a relation between the integral of the Gaussian curvature over a given oriented closed surface S and the topology of S in terms of its Euler number χ(S). Here again, many illustrations are provided to facilitate the reader’s understanding. Chapter 5, Minimal Surfaces, requires some elementary knowledge of complex analysis. However, the author retained the introductory nature of this book and focused on detailed explanations of the examples of minimal surfaces given in Chapter 2.

Author : Francis Bonahon
Publisher : American Mathematical Soc.
Page : 403 pages
File Size : 43,7 Mb
Release : 2009-07-14
Category : Mathematics
ISBN : 9780821848166

Get Book

Low-Dimensional Geometry by Francis Bonahon Pdf

The study of 3-dimensional spaces brings together elements from several areas of mathematics. The most notable are topology and geometry, but elements of number theory and analysis also make appearances. In the past 30 years, there have been striking developments in the mathematics of 3-dimensional manifolds. This book aims to introduce undergraduate students to some of these important developments. Low-Dimensional Geometry starts at a relatively elementary level, and its early chapters can be used as a brief introduction to hyperbolic geometry. However, the ultimate goal is to describe the very recently completed geometrization program for 3-dimensional manifolds. The journey to reach this goal emphasizes examples and concrete constructions as an introduction to more general statements. This includes the tessellations associated to the process of gluing together the sides of a polygon. Bending some of these tessellations provides a natural introduction to 3-dimensional hyperbolic geometry and to the theory of kleinian groups, and it eventually leads to a discussion of the geometrization theorems for knot complements and 3-dimensional manifolds. This book is illustrated with many pictures, as the author intended to share his own enthusiasm for the beauty of some of the mathematical objects involved. However, it also emphasizes mathematical rigor and, with the exception of the most recent research breakthroughs, its constructions and statements are carefully justified.

Author : A. B. Katok,Vaughn Climenhaga
Publisher : American Mathematical Soc.
Page : 307 pages
File Size : 40,6 Mb
Release : 2008
Category : Surfaces
ISBN : 9780821846797

Get Book

Lectures on Surfaces by A. B. Katok,Vaughn Climenhaga Pdf

Summary: Surfaces are among the most common and easily visualized mathematical objects, and their study brings into focus fundamental ideas, concepts, and methods from geometry, topology, complex analysis, Morse theory, and group theory. This book introduces many of the principal actors - the round sphere, flat torus, Mobius strip, and Klein bottle.

Author : Jonathan L Gross,Jay Yellen,Mark Anderson
Publisher : CRC Press
Page : 526 pages
File Size : 42,6 Mb
Release : 2023-05-24
Category : Mathematics
ISBN : 9781000884067

Get Book

Topics in Graph Theory by Jonathan L Gross,Jay Yellen,Mark Anderson Pdf

The interplay continues to grow between graph theory and a wide variety of models and applications in mathematics, computer science, operations research, and the natural and social sciences. Topics in Graph Theory is geared toward the more mathematically mature student. The first three chapters provide the basic definitions and theorems of graph theory and the remaining chapters introduce a variety of topics and directions for research. These topics draw on numerous areas of theoretical and applied mathematics, including combinatorics, probability, linear algebra, group theory, topology, operations research, and computer science. This makes the book appropriate for a first course at the graduate level or as a second course at the undergraduate level. The authors build upon material previously published in Graph Theory and Its Applications, Third Edition, by the same authors. That text covers material for both an undergraduate and graduate course, while this book builds on and expands the graduate-level material. Features Extensive exercises and applications. Flexibility: appropriate for either a first course at the graduate level or an advanced course at the undergraduate level. Opens avenues to a variety of research areas in graph theory. Emphasis on topological and algebraic graph theory.