Applications of Algebraic Topology

Applications of Algebraic Topology
Author :
Publisher : Springer Science & Business Media
Total Pages : 190
Release :
ISBN-10 : 9781468493672
ISBN-13 : 1468493671
Rating : 4/5 (671 Downloads)

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.


Applications of Algebraic Topology Related Books

Applications of Algebraic Topology
Language: en
Pages: 190
Authors: S. Lefschetz
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This monograph is based, in part, upon lectures given in the Princeton School of Engineering and Applied Science. It presupposes mainly an elementary knowledge
Algebraic Topology of Finite Topological Spaces and Applications
Language: en
Pages: 184
Authors: Jonathan A. Barmak
Categories: Mathematics
Type: BOOK - Published: 2011-08-24 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction b
Basic Algebraic Topology and its Applications
Language: en
Pages: 628
Authors: Mahima Ranjan Adhikari
Categories: Mathematics
Type: BOOK - Published: 2016-09-16 - Publisher: Springer

DOWNLOAD EBOOK

This book provides an accessible introduction to algebraic topology, a field at the intersection of topology, geometry and algebra, together with its applicatio
Combinatorial Algebraic Topology
Language: en
Pages: 416
Authors: Dimitry Kozlov
Categories: Mathematics
Type: BOOK - Published: 2008-01-08 - Publisher: Springer Science & Business Media

DOWNLOAD EBOOK

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 t
Topology and Robotics
Language: en
Pages: 202
Authors: Michael Farber
Categories: Mathematics
Type: BOOK - Published: 2007 - Publisher: American Mathematical Soc.

DOWNLOAD EBOOK

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 o