Applications Of Algebraic Topology

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Applications of Algebraic Topology

Author : S. Lefschetz
Publisher : Springer Science & Business Media
ISBN 13 : 1468493671
Total Pages : 190 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Applications of Algebraic Topology by : S. Lefschetz

Download or read book Applications of Algebraic Topology written by S. Lefschetz and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge of linear algebra and of topology. In topology the limit is dimension two mainly in the latter chapters and questions of topological invariance are carefully avoided. From the technical viewpoint graphs is our only requirement. However, later, questions notably related to Kuratowski's classical theorem have demanded an easily provided treatment of 2-complexes and surfaces. January 1972 Solomon Lefschetz 4 INTRODUCTION The study of electrical networks rests upon preliminary theory of graphs. In the literature this theory has always been dealt with by special ad hoc methods. My purpose here is to show that actually this theory is nothing else than the first chapter of classical algebraic topology and may be very advantageously treated as such by the well known methods of that science. Part I of this volume covers the following ground: The first two chapters present, mainly in outline, the needed basic elements of linear algebra. In this part duality is dealt with somewhat more extensively. In Chapter III the merest elements of general topology are discussed. Graph theory proper is covered in Chapters IV and v, first structurally and then as algebra. Chapter VI discusses the applications to networks. In Chapters VII and VIII the elements of the theory of 2-dimensional complexes and surfaces are presented.

Algebraic Topology of Finite Topological Spaces and Applications

Author : Jonathan A. Barmak
Publisher : Springer Science & Business Media
ISBN 13 : 3642220029
Total Pages : 184 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Algebraic Topology of Finite Topological Spaces and Applications by : Jonathan A. Barmak

Download or read book Algebraic Topology of Finite Topological Spaces and Applications written by Jonathan A. Barmak and published by Springer Science & Business Media. This book was released on 2011-08-24 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen's conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.

A Concise Course in Algebraic Topology

Author : J. P. May
Publisher : University of Chicago Press
ISBN 13 : 9780226511832
Total Pages : 262 pages
Book Rating : 4.5/5 (118 download)

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Book Synopsis A Concise Course in Algebraic Topology by : J. P. May

Download or read book A Concise Course in Algebraic Topology written by J. P. May and published by University of Chicago Press. This book was released on 1999-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Basic Algebraic Topology and its Applications

Author : Mahima Ranjan Adhikari
Publisher : Springer
ISBN 13 : 813222843X
Total Pages : 615 pages
Book Rating : 4.1/5 (322 download)

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Book Synopsis Basic Algebraic Topology and its Applications by : Mahima Ranjan Adhikari

Download or read book Basic Algebraic Topology and its Applications written by Mahima Ranjan Adhikari and published by Springer. This book was released on 2016-09-16 with total page 615 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book offers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study.

Essentials of Topology with Applications

Author : Steven G. Krantz
Publisher : CRC Press
ISBN 13 : 1420089757
Total Pages : 422 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Essentials of Topology with Applications by : Steven G. Krantz

Download or read book Essentials of Topology with Applications written by Steven G. Krantz and published by CRC Press. This book was released on 2009-07-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: Brings Readers Up to Speed in This Important and Rapidly Growing AreaSupported by many examples in mathematics, physics, economics, engineering, and other disciplines, Essentials of Topology with Applications provides a clear, insightful, and thorough introduction to the basics of modern topology. It presents the traditional concepts of topological

Combinatorial Algebraic Topology

Author : Dimitry Kozlov
Publisher : Springer Science & Business Media
ISBN 13 : 9783540730514
Total Pages : 416 pages
Book Rating : 4.7/5 (35 download)

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Book Synopsis Combinatorial Algebraic Topology by : Dimitry Kozlov

Download or read book Combinatorial Algebraic Topology written by Dimitry Kozlov and published by Springer Science & Business Media. This book was released on 2008-01-08 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the first comprehensive treatment of combinatorial algebraic topology in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology. Readers - graduate students and working mathematicians alike - will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms.

Topology and Robotics

Author : Michael Farber
Publisher : American Mathematical Soc.
ISBN 13 : 0821842463
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Topology and Robotics by : Michael Farber

Download or read book Topology and Robotics written by Michael Farber and published by American Mathematical Soc.. This book was released on 2007 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lecture Notes in Algebraic Topology

Author : James F. Davis
Publisher : American Mathematical Society
ISBN 13 : 1470473682
Total Pages : 385 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Lecture Notes in Algebraic Topology by : James F. Davis

Download or read book Lecture Notes in Algebraic Topology written by James F. Davis and published by American Mathematical Society. This book was released on 2023-05-22 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The amount of algebraic topology a graduate student specializing in topology must learn can be intimidating. Moreover, by their second year of graduate studies, students must make the transition from understanding simple proofs line-by-line to understanding the overall structure of proofs of difficult theorems. To help students make this transition, the material in this book is presented in an increasingly sophisticated manner. It is intended to bridge the gap between algebraic and geometric topology, both by providing the algebraic tools that a geometric topologist needs and by concentrating on those areas of algebraic topology that are geometrically motivated. Prerequisites for using this book include basic set-theoretic topology, the definition of CW-complexes, some knowledge of the fundamental group/covering space theory, and the construction of singular homology. Most of this material is briefly reviewed at the beginning of the book. The topics discussed by the authors include typical material for first- and second-year graduate courses. The core of the exposition consists of chapters on homotopy groups and on spectral sequences. There is also material that would interest students of geometric topology (homology with local coefficients and obstruction theory) and algebraic topology (spectra and generalized homology), as well as preparation for more advanced topics such as algebraic $K$-theory and the s-cobordism theorem. A unique feature of the book is the inclusion, at the end of each chapter, of several projects that require students to present proofs of substantial theorems and to write notes accompanying their explanations. Working on these projects allows students to grapple with the “big picture”, teaches them how to give mathematical lectures, and prepares them for participating in research seminars. The book is designed as a textbook for graduate students studying algebraic and geometric topology and homotopy theory. It will also be useful for students from other fields such as differential geometry, algebraic geometry, and homological algebra. The exposition in the text is clear; special cases are presented over complex general statements.

Algebraic Topology

Author : C. R. F. Maunder
Publisher : Courier Corporation
ISBN 13 : 9780486691312
Total Pages : 414 pages
Book Rating : 4.6/5 (913 download)

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Book Synopsis Algebraic Topology by : C. R. F. Maunder

Download or read book Algebraic Topology written by C. R. F. Maunder and published by Courier Corporation. This book was released on 1996-01-01 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on lectures to advanced undergraduate and first-year graduate students, this is a thorough, sophisticated, and modern treatment of elementary algebraic topology, essentially from a homotopy theoretic viewpoint. Author C.R.F. Maunder provides examples and exercises; and notes and references at the end of each chapter trace the historical development of the subject.

Quadratic Forms with Applications to Algebraic Geometry and Topology

Author : Albrecht Pfister
Publisher : Cambridge University Press
ISBN 13 : 0521467551
Total Pages : 191 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Quadratic Forms with Applications to Algebraic Geometry and Topology by : Albrecht Pfister

Download or read book Quadratic Forms with Applications to Algebraic Geometry and Topology written by Albrecht Pfister and published by Cambridge University Press. This book was released on 1995-09-28 with total page 191 pages. Available in PDF, EPUB and Kindle. Book excerpt: A gem of a book bringing together 30 years worth of results that are certain to interest anyone whose research touches on quadratic forms.

Applications of Algebraic Topology

Author : S. Lefschetz
Publisher :
ISBN 13 : 9781468493689
Total Pages : 204 pages
Book Rating : 4.4/5 (936 download)

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Book Synopsis Applications of Algebraic Topology by : S. Lefschetz

Download or read book Applications of Algebraic Topology written by S. Lefschetz and published by . This book was released on 2014-01-15 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Topology

Author : Edwin H. Spanier
Publisher : Springer Science & Business Media
ISBN 13 : 1468493221
Total Pages : 548 pages
Book Rating : 4.4/5 (684 download)

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Book Synopsis Algebraic Topology by : Edwin H. Spanier

Download or read book Algebraic Topology written by Edwin H. Spanier and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 548 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the fundamental ideas of algebraic topology. The first part covers the fundamental group, its definition and application in the study of covering spaces. The second part turns to homology theory including cohomology, cup products, cohomology operations and topological manifolds. The final part is devoted to Homotropy theory, including basic facts about homotropy groups and applications to obstruction theory.

Algebraic Topology

Author : Allen Hatcher
Publisher : Cambridge University Press
ISBN 13 : 9780521795401
Total Pages : 572 pages
Book Rating : 4.7/5 (954 download)

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Book Synopsis Algebraic Topology by : Allen Hatcher

Download or read book Algebraic Topology written by Allen Hatcher and published by Cambridge University Press. This book was released on 2002 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introductory textbook suitable for use in a course or for self-study, featuring broad coverage of the subject and a readable exposition, with many examples and exercises.

Algebraic Topology

Author : Tammo tom Dieck
Publisher : European Mathematical Society
ISBN 13 : 9783037190487
Total Pages : 584 pages
Book Rating : 4.1/5 (94 download)

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Book Synopsis Algebraic Topology by : Tammo tom Dieck

Download or read book Algebraic Topology written by Tammo tom Dieck and published by European Mathematical Society. This book was released on 2008 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is written as a textbook on algebraic topology. The first part covers the material for two introductory courses about homotopy and homology. The second part presents more advanced applications and concepts (duality, characteristic classes, homotopy groups of spheres, bordism). The author recommends starting an introductory course with homotopy theory. For this purpose, classical results are presented with new elementary proofs. Alternatively, one could start more traditionally with singular and axiomatic homology. Additional chapters are devoted to the geometry of manifolds, cell complexes and fibre bundles. A special feature is the rich supply of nearly 500 exercises and problems. Several sections include topics which have not appeared before in textbooks as well as simplified proofs for some important results. Prerequisites are standard point set topology (as recalled in the first chapter), elementary algebraic notions (modules, tensor product), and some terminology from category theory. The aim of the book is to introduce advanced undergraduate and graduate (master's) students to basic tools, concepts and results of algebraic topology. Sufficient background material from geometry and algebra is included.

Algebraic Topology from a Homotopical Viewpoint

Author : Marcelo Aguilar
Publisher : Springer Science & Business Media
ISBN 13 : 0387224890
Total Pages : 499 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Algebraic Topology from a Homotopical Viewpoint by : Marcelo Aguilar

Download or read book Algebraic Topology from a Homotopical Viewpoint written by Marcelo Aguilar and published by Springer Science & Business Media. This book was released on 2008-02-02 with total page 499 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.

Applications of Algebraic Topology

Author : Solomon Lefschetz
Publisher :
ISBN 13 :
Total Pages : 190 pages
Book Rating : 4.:/5 (11 download)

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Book Synopsis Applications of Algebraic Topology by : Solomon Lefschetz

Download or read book Applications of Algebraic Topology written by Solomon Lefschetz and published by . This book was released on 1975 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Directed Algebraic Topology and Concurrency

Author : Lisbeth Fajstrup
Publisher : Springer
ISBN 13 : 3319153986
Total Pages : 167 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Directed Algebraic Topology and Concurrency by : Lisbeth Fajstrup

Download or read book Directed Algebraic Topology and Concurrency written by Lisbeth Fajstrup and published by Springer. This book was released on 2016-03-02 with total page 167 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an application of concepts and methods from algebraic topology to models of concurrent processes in computer science and their analysis. Taking well-known discrete models for concurrent processes in resource management as a point of departure, the book goes on to refine combinatorial and topological models. In the process, it develops tools and invariants for the new discipline directed algebraic topology, which is driven by fundamental research interests as well as by applications, primarily in the static analysis of concurrent programs. The state space of a concurrent program is described as a higher-dimensional space, the topology of which encodes the essential properties of the system. In order to analyse all possible executions in the state space, more than “just” the topological properties have to be considered: Execution paths need to respect a partial order given by the time flow. As a result, tools and concepts from topology have to be extended to take privileged directions into account. The target audience for this book consists of graduate students, researchers and practitioners in the field, mathematicians and computer scientists alike.