How Surfaces Intersect In Space: An Introduction To Topology PDF Download

Author: J Scott Carter
Publisher: World Scientific
ISBN: 9814505323
Category : Mathematics
Languages : en
Pages : 301

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Book Description
This is a book of marvelous pictures that illustrates standard examples in low dimensional topology. The text starts at the most basic level (the intersection of coordinate planes) and gives hands on constructions of the most beautiful examples in topology: the projective plane, Poincare's example of a homology sphere, lens spaces, knotted surfaces, 2-sphere eversions, and higher dimensional manifolds. The text carefully explains the importance of the examples and the techniques without being bogged down in a morass of technicalities.Chapter 1 opens with the classification of orientable surfaces, and the meaning of space. Chapter 2 discusses examples of non-orientable surfaces including models of the projective plane and the Klein bottle. Chapter 3 discusses how curves fit on surfaces and gives a general discussion of knotted strings in space. In Chapter 4, some examples of other 3-dimensional spaces are described. These include the 3-dimensional sphere, lens spaces, and the quaternionic projective space. In Chapter 5, the author reviews the movie techniques of studying surfaces in 4-dimensions. He shows how to move among the standard examples of Klein bottles, and he gives a “movie move” decomposition of turning the 2-sphere inside out. In the final Chapter, higher dimensional spaces are examined from the same elementary point of view.The book is a guide book to a wide variety of topics. It will be of value to undergraduates who want to learn geometric topology and to graduate students who want examples with which they can make computations and who need an elementary description of topological spaces. Finally, the book should be interesting to other scientists and mathematicians who want to learn some examples of topological spaces.

Author: J. Scott Carter
Publisher: World Scientific
ISBN: 9789810220662
Category : Science
Languages : en
Pages : 344

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Book Description
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: J. Scott Carter
Publisher: American Mathematical Society
ISBN: 1470476339
Category : Mathematics
Languages : en
Pages : 273

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Book Description
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: J. Scott Carter
Publisher: World Scientific
ISBN: 9814374504
Category : Mathematics
Languages : en
Pages : 294

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Book Description
1. A sphere -- 2. Surfaces, folds, and cusps -- 3. The inside and outside -- 4. Dimensions -- 5. Immersed surfaces -- 6. Movies -- 7. Movie moves -- 8. Taxonomic summary -- 9. How not to turn the sphere inside-out -- 10. A physical metaphor -- 11. Sarah's thesis -- 12. The eversion -- 13. The double point and fold surfaces

Author: Pablo Lorenzo-Eiroa
Publisher: Taylor & Francis
ISBN: 1000882667
Category : Architecture
Languages : en
Pages : 491

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Book Description
This book proposes a new critical relationship between computation and architecture, developing a history and theory of representation in architecture to understand and unleash potential means to open up creativity in the field. Historically, architecture has led to spatial representation. Today, computation has established new representational paradigms that can be compared to spatial representations, such as the revolution of perspective in the Renaissance. Architects now use software, robotics, and fabrication tools with very little understanding and participation in how these tools influence, revolutionize, and determine both architecture and its construction today. Why does the discipline of architecture not have a higher degree of authorship in the conception and development of computational technologies that define spatial representation? This book critically explores the relationship between history, theory, and cultural criticism. Lorenzo-Eiroa positions new understandings through parallel historical sections and theories of many revolutionary representational architecture canons displaced by conventional spatial projection. He identifies the architects, artists, mathematicians, and philosophers that were able to revolutionize their disciplines through the development of new technologies, new systems of representation, and new lenses to understand reality. This book frames the discussion by addressing new means to understand and expand architecture authorship in relation to the survey, information, representation, higher dimensional space, Big Data, and Artificial Intelligence – in the pursuit of activating an architecture of information. This will be important reading for upper-level students and researchers of architecture and architectural theory, especially those with a keen interest in computational design and robotic fabrication.

Author: Gerald Sommer
Publisher: Springer Science & Business Media
ISBN: 9783540635178
Category : Computers
Languages : en
Pages : 412

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Book Description
The book constitutes the refereed proceedings of the International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC '97, held in Kiel, Germany, in September 1997. The volume presents 12 revised full papers carefully reviewed and selected for inclusion in the book. Also included are 10 full invited papers by leading researchers in the area providing a representative state-of-the-art assessment of this rapidly growing field. The papers are organized in topical sections on PAC systems, low level and early vision, recognition of visual structure, processing of 3D visual space, representation and shape perception, inference and action, and visual and motor neurocomputation.

Author: Bianca Falcidieno
Publisher: Springer Science & Business Media
ISBN: 3642781144
Category : Computers
Languages : en
Pages : 465

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Book Description
In the history of technology, many fields have passed from an initial stage of empirical recipes to a mature stage where work is based on formal theories and procedures. This transition is made possible through a process called "modeling". Also Computer Graphics as a separate field of Computer Science makes extensive use of formal theories and procedures of modeling, often derived from related disciplines such as mathematics and physics. Modeling makes different application results consistent, unifying varieties of techniques and formal approaches into a smaller number of models by generalizing and abstracting the knowledge in Computer Graphics. This volume presents a selection of research papers submitted to the conference "Modeling in Computer Graphics: Methods and Applications" held at the Research Area of the National Research Council in Genoa, Italy, on June 28 -July 1, 1993. This meeting was the ideal continuation of a previous conference organized in Tokyo, Japan, in April 1991. The success and the variety of research themes discussed at that meeting suggested to promote a new working conference on methods and applications of modeling to be held in Italy two years later.

Author: Ted Janssen
Publisher: Oxford University Press
ISBN: 0192557815
Category : Science
Languages : en
Pages : 547

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Book Description
Over the past several decades, a This book deals with the characterisation of the structure, the structure determination and the study of the physical properties, especially dynamical and electronic properties of aperiodic crystals. The treatment is based on a description in a space with more dimensions than three, the so-called superspace. This allows us to generalise the standard crystallography and to look differently at the dynamics. The three main classes of aperiodic crystals, modulated phases, incommensurate composites and quasicrystals are treated from a unified point of view, which stresses similarities of the various systems. The book assumes as a prerequisite a knowledge of the fundamental techniques of crystallography and the theory of condensed matter, and covers the literature at the forefront of the field. Since the first edition of this book in 2007, the field of aperiodic crystals has developed considerably, with the discovery of new materials and new structures. Progress has been made in structure determination, in the interpretation and understanding of the structural characteristics and in the calculation of electrons and phonons. This new edition reflects these new developments, and it includes discussions of natural quasicrystals, incommensurate magnetic and multiferroic structures, photonic and mesoscopic quasicrystals. The second edition also includes a number of new exercises that give the reader an opportunityt to check their understanding of the material.

Author: René Alt
Publisher: Springer Science & Business Media
ISBN: 3540212604
Category : Computers
Languages : en
Pages : 324

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Book Description
This book constitutes the thoroughly refereed post-proceedings of the Dagstuhl Seminar 03041 on Numerical Software with Result Verification held at Dagstuhl Castle, Germany, in January 2003. The 18 revised full papers presented were selected during two rounds of reviewing and improvements. The papers are organized in topical sections on languages, software systems and tools, new verification techniques based on interval arithmetic, applications in science and engineering, and novel approaches to verification.

Author: Hiroshi Toriya
Publisher: Springer Science & Business Media
ISBN: 3642457290
Category : Computers
Languages : en
Pages : 284

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Book Description
3D CAD is one of the most important technologies of the 90s for the engineering and manufacturing world. 3D CAD systems can provide a competitive edge in the development of new products. This book presents the development of a three-dimensional CAD system and its wide range of applications. It describes the concepts of solid models, and the theory of curves and surfaces and it illustrates these concepts through "reals world" applications.