These lecture notes are the content of an introductory course on modern, coordinatefree differential geometry which is taken by firstyear theoretical physics PhD students, or by students attending the oneyear MSc course, "Fundamental Fields and Forces" at Imperial College. The book is concerned entirely with mathematics proper, although the emphasis and detailed topics have been chosen bearing in mind the way in which differential geometry is applied to modern theoretical physics. This includes not only the traditional area of general relativity but also the theory of YangMills fields, nonlinear sigma models and other types of nonlinear field systems that feature in modern quantum field theory. This edition of the text contains an additional chapter that introduces some of the basic ideas of general topology needed in differential geometry. A number of small corrections and additions have also been made. The volume is divided into four parts. The first provides an introduction to general topology, the second covers introductory coordinatefree differential geometry, the third examines geometrical aspects of the theory of Lie groups and Lie group actions on manifolds, and the fourth provides an introduction to the theory of fibre bundles. In the introduction to differential geometry the author lays considerable stress on the basic ideas of "tangent space structure", which he develops from several different points of view  some geometrical, others more algebraic.
About C. J. Isham
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Author  :  C. J. Isham 
Publisher  :  World Scientific Publishing Co Pte Ltd 
Data Published  :  23 March 1999 
ISBN  :  9810235623 
EAN  :  9789810235628 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  304 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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