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Author: Solomon Lefschetz
Publisher: American Mathematical Soc.
ISBN: 0821846035
Category : Mathematics
Languages : en
Pages : 428
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Book Description
Lefschetz's Topology was written in the period in between the beginning of topology, by Poincare, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of algebraic varieties. He also gives applications to vector distributions, complex spaces, and Kronecker's characteristic theory.
Author: Solomon Lefschetz
Publisher: American Mathematical Soc.
ISBN: 0821846035
Category : Mathematics
Languages : en
Pages : 428
Get Book Here
Book Description
Lefschetz's Topology was written in the period in between the beginning of topology, by Poincare, and the establishment of algebraic topology as a well-formed subject, separate from point-set or geometric topology. At this time, Lefschetz had already proved his first fixed-point theorems. In some sense, the present book is a description of the broad subject of topology into which Lefschetz's theory of fixed points fits. Lefschetz takes the opportunity to describe some of the important applications of his theory, particularly in algebraic geometry, to problems such as counting intersections of algebraic varieties. He also gives applications to vector distributions, complex spaces, and Kronecker's characteristic theory.
Author: Solomon Lefschetz
Publisher: Princeton University Press
ISBN: 1400882338
Category : Mathematics
Languages : en
Pages : 137
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Book Description
Solomon Lefschetz pioneered the field of topology--the study of the properties of manysided figures and their ability to deform, twist, and stretch without changing their shape. According to Lefschetz, "If it's just turning the crank, it's algebra, but if it's got an idea in it, it's topology." The very word topology comes from the title of an earlier Lefschetz monograph published in 1920. In Topics in Topology Lefschetz developed a more in-depth introduction to the field, providing authoritative explanations of what would today be considered the basic tools of algebraic topology. Lefschetz moved to the United States from France in 1905 at the age of twenty-one to find employment opportunities not available to him as a Jew in France. He worked at Westinghouse Electric Company in Pittsburgh and there suffered a horrible laboratory accident, losing both hands and forearms. He continued to work for Westinghouse, teaching mathematics, and went on to earn a Ph.D. and to pursue an academic career in mathematics. When he joined the mathematics faculty at Princeton University, he became one of its first Jewish faculty members in any discipline. He was immensely popular, and his memory continues to elicit admiring anecdotes. Editor of Princeton University Press's Annals of Mathematics from 1928 to 1958, Lefschetz built it into a world-class scholarly journal. He published another book, Lectures on Differential Equations, with Princeton in 1946.
Author: Solomon Lefschetz
Publisher: Princeton University Press
ISBN: 1400879949
Category : Mathematics
Languages : en
Pages : 227
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Book Description
In this book, which may be used as a self-contained text for a beginning course, Professor Lefschetz aims to give the reader a concrete working knowledge of the central concepts of modern combinatorial topology: complexes, homology groups, mappings in spheres, homotopy, transformations and their fixed points, manifolds and duality theorems. Each chapter ends with a group of problems. Originally published in 1949. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Author: S. Lefschetz
Publisher: Springer Science & Business Media
ISBN: 1468493671
Category : Mathematics
Languages : en
Pages : 190
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Book Description
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.
Author: Solomon Lefschetz
Publisher: Courier Corporation
ISBN: 0486154726
Category : Mathematics
Languages : en
Pages : 250
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Book Description
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Author: Solomon Lefschetz
Publisher:
ISBN: 9781258544249
Category :
Languages : en
Pages : 398
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Book Description
Author: Solomon Lefschetz
Publisher: American Mathematical Soc.
ISBN: 0821810278
Category : Mathematics
Languages : en
Pages : 404
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Book Description
Author: Solomon Lefschetz
Publisher:
ISBN:
Category : Topology
Languages : en
Pages : 410
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Book Description
Author: I.M. James
Publisher: Elsevier
ISBN: 0080534074
Category : Mathematics
Languages : en
Pages : 1067
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Book Description
Topology, for many years, has been one of the most exciting and influential fields of research in modern mathematics. Although its origins may be traced back several hundred years, it was Poincaré who "gave topology wings" in a classic series of articles published around the turn of the century. While the earlier history, sometimes called the prehistory, is also considered, this volume is mainly concerned with the more recent history of topology, from Poincaré onwards.As will be seen from the list of contents the articles cover a wide range of topics. Some are more technical than others, but the reader without a great deal of technical knowledge should still find most of the articles accessible. Some are written by professional historians of mathematics, others by historically-minded mathematicians, who tend to have a different viewpoint.
Author: Haynes R Miller
Publisher: World Scientific
ISBN: 9811231265
Category : Mathematics
Languages : en
Pages : 405
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Book Description
Algebraic Topology and basic homotopy theory form a fundamental building block for much of modern mathematics. These lecture notes represent a culmination of many years of leading a two-semester course in this subject at MIT. The style is engaging and student-friendly, but precise. Every lecture is accompanied by exercises. It begins slowly in order to gather up students with a variety of backgrounds, but gains pace as the course progresses, and by the end the student has a command of all the basic techniques of classical homotopy theory.
