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Applied Mathematical Sciences

Applications of Algebraic Topology

Graphs and Networks. The Picard-Lefschetz Theory and Feynman Integrals

Authors: Lefschetz, S.

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About this book

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.

Table of contents (14 chapters)

Table of contents (14 chapters)

Buy this book

eBook $59.99
price for USA in USD
  • ISBN 978-1-4684-9367-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-0-387-90137-4
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Covid-19 shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Algebraic Topology
Book Subtitle
Graphs and Networks. The Picard-Lefschetz Theory and Feynman Integrals
Authors
Series Title
Applied Mathematical Sciences
Series Volume
16
Copyright
1975
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4684-9367-2
DOI
10.1007/978-1-4684-9367-2
Softcover ISBN
978-0-387-90137-4
Series ISSN
0066-5452
Edition Number
1
Number of Pages
VIII, 191
Topics