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Applications of Algebraic Topology : Graphs and Networks The Picard-Lefschetz Theory and Feynman Integrals

Author: S Lefschetz
Publisher: New York, NY : Springer New York, 1975.
Series: Applied mathematical sciences (Springer-Verlag New York Inc.), 16.
Edition/Format:   eBook : Bibliographic data : English
Summary:
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  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
John, Fritz.
Applications of Algebraic Topology : Graphs and Networks The Picard-Lefschetz Theory and Feynman Integrals.
New York : Springer New York, ©1975
Material Type: Bibliographic data, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: S Lefschetz
ISBN: 9781468493672 1468493671
OCLC Number: 840289974
Description: 1 online resource (202 pages).
Contents: I Application of Classical Topology to Graphs and Networks --
I. A Résumé of Linear Algebra --
II. Duality in Vector Spaces --
III. Topological Preliminaries --
IV. Graphs. Geometric Structure --
V. Graph Algebra --
VI. Electrical Networks --
VII. Complexes --
VIII. Surfaces --
IX. Planar Graphs --
II The Picard-Lefschetz Theory and Feynman Integrals --
I. Topological and Algebraic Considerations --
II. The Picard-Lefschetz Theory --
III. Extension to Higher Varieties --
IV. Feynman Integrals --
V. Feynman Integrals. B --
Subject Index Part I --
Subject Index Part II.
Series Title: Applied mathematical sciences (Springer-Verlag New York Inc.), 16.
Responsibility: by S. Lefschetz.

Abstract:

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.

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