New Scientific Applications Of Geometry And Topology

Author : De Witt L. Sumners,Nicholas R. Cozzarelli
Publisher : American Mathematical Soc.
Page : 266 pages
File Size : 52,5 Mb
Release : 1992
Category : Mathematics
ISBN : 0821855026

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New Scientific Applications of Geometry and Topology by De Witt L. Sumners,Nicholas R. Cozzarelli Pdf

Geometry and topology are subjects generally considered to be "pure" mathematics. Recently, however, some of the methods and results in these two areas have found new utility in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing new connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this book communicates the excitement and utility of mathematics research at an elementary level, it is an excellent textbook in an advanced undergraduate mathematics course.

Author : De Witt L. Sumners
Publisher : American Mathematical Society(RI)
Page : 263 pages
File Size : 53,7 Mb
Release : 2014-05-10
Category : MATHEMATICS
ISBN : 0821892606

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New Scientific Applications of Geometry and Topology by De Witt L. Sumners Pdf

Geometry and topology are subjects generally considered to be pure mathematics. However, some of the methods and results in these two areas have found uses in both wet-lab science (biology and chemistry) and theoretical physics. Conversely, science is influencing mathematics, from posing questions that call for the construction of mathematical models to exporting theoretical methods of attack on long-standing problems of mathematical interest. Based on an AMS Short Course held in January 1992, this book contains six introductory articles on these intriguing connections. There are articles by a chemist and a biologist about mathematics, and four articles by mathematicians writing about science and mathematics involved. Because this collection communicates the utility of mathematics research at an elementary level, it should be a useful textbook for an advanced undergraduate mathematics course.

Author : Mikio Nakahara
Publisher : Taylor & Francis
Page : 596 pages
File Size : 48,5 Mb
Release : 2018-10-03
Category : Mathematics
ISBN : 9781420056945

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Geometry, Topology and Physics by Mikio Nakahara Pdf

Differential geometry and topology have become essential tools for many theoretical physicists. In particular, they are indispensable in theoretical studies of condensed matter physics, gravity, and particle physics. Geometry, Topology and Physics, Second Edition introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. The second edition of this popular and established text incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject. The book features a considerably expanded first chapter, reviewing aspects of path integral quantization and gauge theories. Chapter 2 introduces the mathematical concepts of maps, vector spaces, and topology. The following chapters focus on more elaborate concepts in geometry and topology and discuss the application of these concepts to liquid crystals, superfluid helium, general relativity, and bosonic string theory. Later chapters unify geometry and topology, exploring fiber bundles, characteristic classes, and index theorems. New to this second edition is the proof of the index theorem in terms of supersymmetric quantum mechanics. The final two chapters are devoted to the most fascinating applications of geometry and topology in contemporary physics, namely the study of anomalies in gauge field theories and the analysis of Polakov's bosonic string theory from the geometrical point of view. Geometry, Topology and Physics, Second Edition is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

Author : Michael I. Monastyrsky
Publisher : Springer Science & Business Media
Page : 238 pages
File Size : 42,7 Mb
Release : 2006-10-26
Category : Science
ISBN : 9783540498582

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Topology in Molecular Biology by Michael I. Monastyrsky Pdf

Providing a course of modern topology intended for biologists and physicists, this book presents a class of results in molecular biology for which topological methods and ideas are important. These include: the large-scale conformation properties of DNA; computational methods; the structure of proteins; and other problems in molecular biology.

Author : Helmut Eschrig
Publisher : Springer
Page : 397 pages
File Size : 54,6 Mb
Release : 2011-01-26
Category : Science
ISBN : 9783642147005

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Topology and Geometry for Physics by Helmut Eschrig Pdf

A concise but self-contained introduction of the central concepts of modern topology and differential geometry on a mathematical level is given specifically with applications in physics in mind. All basic concepts are systematically provided including sketches of the proofs of most statements. Smooth finite-dimensional manifolds, tensor and exterior calculus operating on them, homotopy, (co)homology theory including Morse theory of critical points, as well as the theory of fiber bundles and Riemannian geometry, are treated. Examples from physics comprise topological charges, the topology of periodic boundary conditions for solids, gauge fields, geometric phases in quantum physics and gravitation.

Author : Stuart G. Whittington,Witt De Sumners,Timothy Lodge
Publisher : Springer Science & Business Media
Page : 209 pages
File Size : 51,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461217121

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Topology and Geometry in Polymer Science by Stuart G. Whittington,Witt De Sumners,Timothy Lodge Pdf

This IMA Volume in Mathematics and its Applications TOPOLOGY AND GEOMETRY IN POLYMER SCIENCE is based on the proceedings of a very successful one-week workshop with the same title. This workshop was an integral part of the 1995-1996 IMA program on "Mathematical Methods in Materials Science." We would like to thank Stuart G. Whittington, De Witt Sumners, and Timothy Lodge for their excellent work as organizers of the meeting and for editing the proceedings. We also take this opportunity to thank the National Science Foun dation (NSF), the Army Research Office (ARO) and the Office of Naval Research (ONR), whose financial support made the workshop possible. A vner Friedman Robert Gulliver v PREFACE This book is the product of a workshop on Topology and Geometry of Polymers, held at the IMA in June 1996. The workshop brought together topologists, combinatorialists, theoretical physicists and polymer scientists, who share an interest in characterizing and predicting the microscopic en tanglement properties of polymers, and their effect on macroscopic physical properties.

Author : Ilia Itenberg,Burglind Jöricke,Mikael Passare
Publisher : Springer Science & Business Media
Page : 483 pages
File Size : 55,5 Mb
Release : 2011-12-14
Category : Mathematics
ISBN : 9780817682774

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Perspectives in Analysis, Geometry, and Topology by Ilia Itenberg,Burglind Jöricke,Mikael Passare Pdf

The articles in this volume are invited papers from the Marcus Wallenberg symposium and focus on research topics that bridge the gap between analysis, geometry, and topology. The encounters between these three fields are widespread and often provide impetus for major breakthroughs in applications. Topics include new developments in low dimensional topology related to invariants of links and three and four manifolds; Perelman's spectacular proof of the Poincare conjecture; and the recent advances made in algebraic, complex, symplectic, and tropical geometry.

Author : Arkady L Kholodenko
Publisher : World Scientific
Page : 492 pages
File Size : 41,5 Mb
Release : 2013-05-03
Category : Mathematics
ISBN : 9789814412100

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Applications of Contact Geometry and Topology in Physics by Arkady L Kholodenko Pdf

Although contact geometry and topology is briefly discussed in V I Arnol'd's book “Mathematical Methods of Classical Mechanics ”(Springer-Verlag, 1989, 2nd edition), it still remains a domain of research in pure mathematics, e.g. see the recent monograph by H Geiges “An Introduction to Contact Topology” (Cambridge U Press, 2008). Some attempts to use contact geometry in physics were made in the monograph “Contact Geometry and Nonlinear Differential Equations” (Cambridge U Press, 2007). Unfortunately, even the excellent style of this monograph is not sufficient to attract the attention of the physics community to this type of problems. This book is the first serious attempt to change the existing status quo. In it we demonstrate that, in fact, all branches of theoretical physics can be rewritten in the language of contact geometry and topology: from mechanics, thermodynamics and electrodynamics to optics, gauge fields and gravity; from physics of liquid crystals to quantum mechanics and quantum computers, etc. The book is written in the style of famous Landau–Lifshitz (L–L) multivolume course in theoretical physics. This means that its readers are expected to have solid background in theoretical physics (at least at the level of the L–L course). No prior knowledge of specialized mathematics is required. All needed new mathematics is given in the context of discussed physical problems. As in the L–L course some problems/exercises are formulated along the way and, again as in the L–L course, these are always supplemented by either solutions or by hints (with exact references). Unlike the L–L course, though, some definitions, theorems, and remarks are also presented. This is done with the purpose of stimulating the interest of our readers in deeper study of subject matters discussed in the text. Contents:Motivation and BackgroundFrom Ideal Magnetohydrodynamics to String and Knot TheoryAll About and Around Woltjer's TheoremTopologically Massive Gauge Theories and Force-Free FieldsContact Geometry and PhysicsSub-Riemannian Geometry, Heisenberg Manifolds and Quantum Mechanics of Landau LevelsAbrikosov Lattices, TGB Phases in Liquid Crystals and Heisenberg GroupSub-Riemannian Geometry, Spin Dynamics and Quantum-Classical Optimal ControlFrom Contact Geometry to Contact TopologyClosing Remarks:The Unreasonable Effectivenessof Contact Geometry and Topology in Physical SciencesAppendices:Heisenberg Group in the Context of Sub-Riemannian Geometry and Optimal ControlSub-Riemannian Dynamics of Josephson JunctionsQuantum Computers and Quantum Random WalksThe Measurement Protocol. Geometry and Topology of Entanglements Readership: Students in applied mathematics and theoretical physics. Keywords:Force-Free Fields;Contact and Sub-Riemannian Geometry;Optimal Control;Theoretical PhysicsKey Features:This book is the world's first book on contact/sub-Riemannian geometry and topology for physicistsUnlike books discussing mathematical methods for physicists, this book discusses physical problems first and only then uses new mathematics to solve these problems. Problems are selected from practically all branches of theoretical physicsThis is done with the purpose of demonstrating that contact geometry should be looked upon as a universal language/technical tool of theoretical physicsReviews: “This book is written in the style of the well-known Landau-Lifshitz multivolume course in theoretical physics and its prime goal, as the author puts it, is to show the diversity of applications of contact geometry and topology. I enjoyed reading this book, in which the author allows readers to see for themselves “the same forest behind different kinds of trees”. I strongly recommend this book to interested readers.” MathSciNet

Author : Gregory L. Naber
Publisher : Springer Science & Business Media
Page : 410 pages
File Size : 40,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475727425

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Topology, Geometry, and Gauge Fields by Gregory L. Naber Pdf

Like any books on a subject as vast as this, this book has to have a point-of-view to guide the selection of topics. Naber takes the view that the rekindled interest that mathematics and physics have shown in each other of late should be fostered, and that this is best accomplished by allowing them to cohabit. The book weaves together rudimentary notions from the classical gauge theory of physics with the topological and geometrical concepts that became the mathematical models of these notions. The reader is asked to join the author on some vague notion of what an electromagnetic field might be, to be willing to accept a few of the more elementary pronouncements of quantum mechanics, and to have a solid background in real analysis and linear algebra and some of the vocabulary of modern algebra. In return, the book offers an excursion that begins with the definition of a topological space and finds its way eventually to the moduli space of anti-self-dual SU(2) connections on S4 with instanton number -1.

Author : Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones
Publisher : Springer Science & Business Media
Page : 271 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461395263

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Algebraic Topology and Its Applications by Gunnar E. Carlsson,Ralph L. Cohen,Wu-Chung Hsiang,John D.S. Jones Pdf

In 1989-90 the Mathematical Sciences Research Institute conducted a program on Algebraic Topology and its Applications. The main areas of concentration were homotopy theory, K-theory, and applications to geometric topology, gauge theory, and moduli spaces. Workshops were conducted in these three areas. This volume consists of invited, expository articles on the topics studied during this program. They describe recent advances and point to possible new directions. They should prove to be useful references for researchers in Algebraic Topology and related fields, as well as to graduate students.

Author : Tim Maudlin
Publisher : Oxford University Press
Page : 374 pages
File Size : 49,5 Mb
Release : 2014-02
Category : Mathematics
ISBN : 9780198701309

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New Foundations for Physical Geometry by Tim Maudlin Pdf

Tim Maudlin sets out a completely new method for describing the geometrical structure of spaces, and thus a better mathematical tool for describing and understanding space-time. He presents a historical review of the development of geometry and topology, and then his original Theory of Linear Structures.

Author : William F. Basener
Publisher : John Wiley & Sons
Page : 295 pages
File Size : 46,6 Mb
Release : 2013-06-12
Category : Mathematics
ISBN : 9781118626221

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Topology and Its Applications by William F. Basener Pdf

Discover a unique and modern treatment of topology employing a cross-disciplinary approach Implemented recently to understand diverse topics, such as cell biology, superconductors, and robot motion, topology has been transformed from a theoretical field that highlights mathematical theory to a subject that plays a growing role in nearly all fields of scientific investigation. Moving from the concrete to the abstract, Topology and Its Applications displays both the beauty and utility of topology, first presenting the essentials of topology followed by its emerging role within the new frontiers in research. Filling a gap between the teaching of topology and its modern uses in real-world phenomena, Topology and Its Applications is organized around the mathematical theory of topology, a framework of rigorous theorems, and clear, elegant proofs. This book is the first of its kind to present applications in computer graphics, economics, dynamical systems, condensed matter physics, biology, robotics, chemistry, cosmology, material science, computational topology, and population modeling, as well as other areas of science and engineering. Many of these applications are presented in optional sections, allowing an instructor to customize the presentation. The author presents a diversity of topological areas, including point-set topology, geometric topology, differential topology, and algebraic/combinatorial topology. Topics within these areas include: Open sets Compactness Homotopy Surface classification Index theory on surfaces Manifolds and complexes Topological 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 publisher's Web site.

Author : Michael Farber,Markus Burger
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 51,8 Mb
Release : 2007
Category : Robotics
ISBN : 9780821842461

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Topology and Robotics by Michael Farber,Markus Burger Pdf

Ever since the literary works of Capek and Asimov, mankind has been fascinated by the idea of robots. Modern research in robotics reveals that along with many other branches of mathematics, topology has a fundamental role to play in making these grand ideas a reality. This volume summarizes recent progress in the field of topological robotics--a new discipline at the crossroads of topology, engineering and computer science. Currently, topological robotics is developing in two main directions. On one hand, it studies pure topological problems inspired by robotics and engineering. On the other hand, it uses topological ideas, topological language, topological philosophy, and specially developed tools of algebraic topology to solve problems of engineering and computer science. Examples of research in both these directions are given by articles in this volume, which is designed to be a mixture of various interesting topics of pure mathematics and practical engineering.

Author : Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo
Publisher : American Mathematical Soc.
Page : 408 pages
File Size : 52,9 Mb
Release : 2020-10-21
Category : Education
ISBN : 9781470461324

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Geometry and Topology of Manifolds: Surfaces and Beyond by Vicente Muñoz,Ángel González-Prieto,Juan Ángel Rojo Pdf

This book represents a novel approach to differential topology. Its main focus is to give a comprehensive introduction to the classification of manifolds, with special attention paid to the case of surfaces, for which the book provides a complete classification from many points of view: topological, smooth, constant curvature, complex, and conformal. Each chapter briefly revisits basic results usually known to graduate students from an alternative perspective, focusing on surfaces. We provide full proofs of some remarkable results that sometimes are missed in basic courses (e.g., the construction of triangulations on surfaces, the classification of surfaces, the Gauss-Bonnet theorem, the degree-genus formula for complex plane curves, the existence of constant curvature metrics on conformal surfaces), and we give hints to questions about higher dimensional manifolds. Many examples and remarks are scattered through the book. Each chapter ends with an exhaustive collection of problems and a list of topics for further study. The book is primarily addressed to graduate students who did take standard introductory courses on algebraic topology, differential and Riemannian geometry, or algebraic geometry, but have not seen their deep interconnections, which permeate a modern approach to geometry and topology of manifolds.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 50,5 Mb
Release : 2024-06-13
Category : Electronic
ISBN : 9789814479455

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Geometries of Nature, Living Systems and Human Cognition by Anonim Pdf