How Surfaces Intersect In Space An Introduction To Topology
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How Surfaces Intersect In Space An Introduction To Topology
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Author : J Scott Carter
language : en
Publisher: World Scientific
Release Date : 1993-03-09
How Surfaces Intersect In Space An Introduction To Topology written by J Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-03-09 with Mathematics categories.
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.
How Surfaces Intersect In Space An Introduction To Topology 2nd Edition
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Author : J Scott Carter
language : en
Publisher: World Scientific
Release Date : 1995-05-11
How Surfaces Intersect In Space An Introduction To Topology 2nd Edition written by J Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-05-11 with Mathematics categories.
This marvelous book of pictures illustrates the fundamental concepts of geometric topology in a way that is very friendly to the reader. The first chapter discusses the meaning of surface and space and gives the classification of orientable surfaces. In the second chapter we are introduced to the Möbius band and surfaces that can be constructed from this non-orientable piece of fabric. In chapter 3, we see how curves can fit in surfaces and how surfaces can fit into spaces with these curves on their boundary. Basic applications to knot theory are discussed and four-dimensional space is introduced.In Chapter 4 we learn about some 3-dimensional spaces and surfaces that sit inside them. These surfaces help us imagine the structures of the larger space.Chapter 5 is completely new! It contains recent results of Cromwell, Izumiya and Marar. One of these results is a formula relating the rank of a surface to the number of triple points. The other major result is a collection of examples of surfaces in 3-space that have one triple point and 6 branch points. These are beautiful generalizations of the Steiner Roman surface.Chapter 6 reviews the movie technique for examining surfaces in 4-dimensional space. Various movies of the Klein bottle are presented, and the Carter-Saito movie move theorem is explained. The author shows us how to turn the 2-sphere inside out by means of these movie moves and this illustration alone is well worth the price of the book!In the last chapter higher dimensional spaces are examined from an elementary point of view.This is a guide book to a wide variety of topics. 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.
Orbiting The Moons Of Pluto Complex Solutions To The Einstein Maxwell Schrodinger And Dirac Equations
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Author : Richard L Amoroso
language : en
Publisher: World Scientific
Release Date : 2011-03-21
Orbiting The Moons Of Pluto Complex Solutions To The Einstein Maxwell Schrodinger And Dirac Equations written by Richard L Amoroso and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-21 with Science categories.
The Maxwell, Einstein, Schrödinger and Dirac equations are considered the most important equations in all of physics. This volume aims to provide new eight- and twelve-dimensional complex solutions to these equations for the first time in order to reveal their richness and continued importance for advancing fundamental Physics. If M-Theory is to keep its promise of defining the ultimate structure of matter and spacetime, it is only through the topological configurations of additional dimensionality (or degrees of freedom) that this will be possible. Stretching the exploration of complex space through all of the main equations of Physics should help tighten the noose on “the” fundamental theory. This kind of exploration of higher dimensional spacetime has for the most part been neglected by M-theorists and physicists in general and is taken to its penultimate form here.
Functorial Knot Theory
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Author : David N. Yetter
language : en
Publisher: World Scientific
Release Date : 2001
Functorial Knot Theory written by David N. Yetter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.
Almost since the advent of skein-theoretic invariants of knots and links (the Jones, HOMFLY, and Kauffman polynomials), the important role of categories of tangles in the connection between low-dimensional topology and quantum-group theory has been recognized. The rich categorical structures naturally arising from the considerations of cobordisms have suggested functorial views of topological field theory. This book begins with a detailed exposition of the key ideas in the discovery of monoidal categories of tangles as central objects of study in low-dimensional topology. The focus then turns to the deformation theory of monoidal categories and the related deformation theory of monoidal functors, which is a proper generalization of Gerstenhaber''s deformation theory of associative algebras. These serve as the building blocks for a deformation theory of braided monoidal categories which gives rise to sequences of Vassiliev invariants of framed links, and clarify their interrelations. Contents: Knots and Categories: Monoidal Categories, Functors and Natural Transformations; A Digression on Algebras; Knot Polynomials; Smooth Tangles and PL Tangles; A Little Enriched Category Theory; Deformations: Deformation Complexes of Semigroupal Categories and Functors; First Order Deformations; Units; Extrinsic Deformations of Monoidal Categories; Categorical Deformations as Proper Generalizations of Classical Notions; and other papers. Readership: Mathematicians and theoretical physicists.
An Excursion In Diagrammatic Algebra
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Author : J. Scott Carter
language : en
Publisher: World Scientific
Release Date : 2012
An Excursion In Diagrammatic Algebra written by J. Scott Carter and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
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
The Bulletin Of Mathematics Books
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Author :
language : en
Publisher:
Release Date : 1992
The Bulletin Of Mathematics Books written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computer software categories.
The Mathematica Guidebook For Graphics
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Author : Michael Trott
language : en
Publisher: Springer
Release Date : 2017-02-11
The Mathematica Guidebook For Graphics written by Michael Trott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-02-11 with Computers categories.
Mathematica is today’s most advanced technical computing system. It features a rich programming environment, two-and three-dimensional graphics capabilities and hundreds of sophisticated, powerful programming and mathematical functions using state-of-the-art algorithms. Combined with a user-friendly interface, and a complete mathematical typesetting system, Mathematica offers an intuitive, easy-to-handle environment of great power and utility. The Mathematica Guidebook for Graphics provides a comprehensive step-by-step development of how to use Mathematica to visualize functions and data, manipulate graphics, and optimize their appearance. Two-dimensional graphics, contour plots, plots of surfaces, free-form three-dimensional surfaces, and animations are the core topics. Hundreds of detailed examples and programs show a large variety of visualization techniques, algorithms, methods, and tricks. These tools allow the reader to create virtually any possible graphic, from simple curves to scientific visualizations and artistic images and logos. Mathematica graphics functions are discussed in detail, explained in numerous examples, and put to work in programs that are all contained on the accompanying DVD. Unique Features: * Step-by-step introductions to all of Mathematica graphics capabilities * Comprehensive presentation of two-and three-dimensional graphics primitives and directives, as well as plotting capabilities for functions and data * Hundreds of unique and innovative scientific visualizations and artistic images * Website for book with additional materials and updates: http://www.MathematicaGuideBooks.org * Accompanying DVD contains all material as an electronic book with complete, executable Mathematica versions 4 and 5 compatible code and programs, rendered color graphics, and animations Michael Trott is a symbolic computation and computer graphics expert. He holds a Ph.D. in theoretical physics and joined the R&D team at Wolfram Research in 1994, the creators of Mathematica. Since 1998, he has been leading development of the Wolfram Functions Site http://functions.wolfram.com, which currently features more that 80,000 formulas and identities, and thousands of visualizations.
Diamond
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Author : Nathaniel S. Hellerstein
language : en
Publisher: World Scientific
Release Date : 2010
Diamond written by Nathaniel S. Hellerstein and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
This book is about ?diamond?, a logic of paradox. In diamond, a statement can be true yet false; an ?imaginary? state, midway between being and non-being. Diamond's imaginary values solve many logical paradoxes unsolvable in two-valued Boolean logic. In this volume, paradoxes by Russell, Cantor, Berry and Zeno are all resolved. This book has three sections: Paradox Logic, which covers the classic paradoxes of mathematical logic, shows how they can be resolved in this new system; The Second Paradox, which relates diamond to Boolean logic and the Spencer?Brown ?modulator?; and Metamathematical Dilemma, which relates diamond to Gdelian metamathematics and dilemma games.
Energy Of Knots And Conformal Geometry
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Author : Jun O'hara
language : en
Publisher: World Scientific
Release Date : 2003-03-25
Energy Of Knots And Conformal Geometry written by Jun O'hara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-25 with Mathematics categories.
Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments.
Woods Hole Mathematics
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Author : Nils Tongring
language : en
Publisher: World Scientific
Release Date : 2004
Woods Hole Mathematics written by Nils Tongring and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
The central theme of this volume is the contemporary mathematics of geometry and physics, but the work also discusses the problem of the secondary structure of proteins, and an overview of arc complexes with proposed applications to macromolecular folding is given.?Woods Hole has played such a vital role in both my mathematical and personal life that it is a great pleasure to see the mathematical tradition of the 1964 meeting resurrected forty years later and, as this volume shows, resurrected with new vigor and hopefully on a regular basis. I therefore consider it a signal honor to have been asked to introduce this volume with a few reminiscences of that meeting forty years ago.? Introduction by R Bott (Wolf Prize Winner, 2000).