Topology, Geometry and Gauge fields: Foundations 2e

Topology, Geometry and Gauge fields: Foundations 2nd Edition PDF Download Ebook. Gregory L. 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.

This is a book on topology and geometry, and like any book on subjects as vast as these, it has a point of view that guided the selection of topics. The author’s point of view is 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 goal is to weave together rudimentary notions from the classical gauge theories of physics and the topological and geometrical concepts that became the mathematical models of these notions. The reader is assumed to have a minimal understanding of what an electromagnetic field is, a willingness to accept a few of the more elementary pronouncements of quantum mechanics, and a solid background in real analysis and linear algebra with some of the vocabulary of modern algebra.

To such a reader we offer 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. It includes a new chapter on singular homology theory and a new appendix outlining Donaldson’s beautiful application of gauge theory to the topology of compact, simply connected , smooth 4-manifolds with definite intersection form.

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Essential Topology by Martin D. Crossley

Essential Topology PDF Download Ebook. Martin D. Crossley brings the most important aspects of modern topology within reach of a second-year undergraduate student. It successfully unites the most exciting aspects of modern topology with those that are most useful for research, leaving readers prepared and motivated for further study.

This book presents the most important aspects of modern topology, essential subjects of research in algebraic topology. The book contains all the key results of basic topology and the focus throughout on providing interesting examples that clarify the ideas and motivate the student. It contains enough material for two-semester courses and offers interesting material for undergraduate-level topology, motivating students for post-graduate study in the field and giving them a solid foundation.

This text provides a concise and well-focused introduction to point set and algebraic topology. The main purpose is to quickly move to relevant notions from algebraic topology (homotopy and homology). Throughout the book the author has taken great care to explain topological concepts by well-chosen examples. It is written in a clear and pleasant style and can certainly be recommended as a basis for an introductory course on the subject.

Written from a thoroughly modern perspective, every topic is introduced with an explanation of why it is being studied, and a huge number of examples provide further motivation. The book is ideal for self-study and assumes only a familiarity with the notion of continuity and basic algebra.

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Introduction to Topology: Pure and Applied, Colin Adams

Introduction to Topology: Pure and Applied PDF Download Ebook. Colin Adams and Robert Franzosa describe the basics of point-set topology with the understanding of its real-world application to a variety of other subjects including science, economics, engineering, and other areas of mathematics.

This book introduces topology as an important and fascinating mathematics discipline to retain the readers interest in the subject. Written in an accessible way for readers to understand the usefulness and importance of the application of topology to other fields, this book introduces topology concepts combined with their real-world application to subjects such DNA, heart stimulation, population modeling, cosmology, and computer graphics.

Author covers topics including knot theory, degree theory, dynamical systems and chaos, graph theory, metric spaces, connectedness, and compactness. It is useful reference for readers wanting an intuitive introduction to topology. Numerous figures allow students to visualize and understand the material presented.

The authors focus on the basic concepts of topology and their utility using real-world applications. Applications cover a wide variety of disciplines, including molecular biology, digital image processing, robotics, population dynamics, medicine, economics, synthetic chemistry, electronic circuit design, and cosmology.

Intuitive and accessibly written text, this book offers rigorous presentation of the mathematics with intuitive descriptions and discussions to increase student understand. Examples of real world application keep students engrossed in the material.

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Topology 2nd Edition by James Munkres

Topology 2nd Edition PDF Download Ebook. James Munkres provides separate, in-depth coverage of both general topology and algebraic topology with many examples and figures. This text is designed to provide instructors with a convenient single text resource for bridging between general and algebraic topology courses.

Two separate, distinct sections (one on general, point set topology, the other on algebraic topology) are each suitable for a one-semester course and are based around the same set of basic, core topics. Optional, independent topics and applications can be studied and developed in depth depending on course needs and preferences.

What follows is a wealth of applications-to the topology of the plane (including the Jordan curve theorem), to the classification of compact surfaces, and to the classification of covering spaces. A final chapter provides an application to group theory itself. This book follows the present-day trend in the teaching of topology which explores the subject much more extensively with one semester devoted to general topology and a second to algebraic topology.

Order of topics proceeds naturally from the familiar to the unfamiliar begins with the familiar set theory, moves on to a thorough and careful treatment of topological spaces, then explores connectedness and compactness (with their many ties to calculus and analysis), and then branches out to the new and different topics mentioned above.

Author carefully guides students through transitions to more advanced topics being careful not to overwhelm them. Each of the text's two parts is suitable for a one-semester course, giving instructors a convenient single text resource for bridging between the courses. The text can also be used where algebraic topology is studied only briefly at the end of a single-semester course.

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Geometry, Topology and Physics 2nd Edition, Nakahara

Geometry, Topology and Physics 2nd Edition PDF Download Ebook. Mikio Nakahara describes 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.

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. This book introduces the ideas and techniques of differential geometry and topology at a level suitable for postgraduate students and researchers in these fields. It incorporates a number of changes designed to meet the needs of the reader and reflect the development of the subject.

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. It is an ideal introduction to differential geometry and topology for postgraduate students and researchers in theoretical and mathematical physics.

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