By Itkin A.L., Kolesnichenko E.G.
Those lecture notes are the content material of an introductory direction on smooth, co-ordinate-free differential geometry that is taken by means of first-year theoretical physics PhD scholars, or by way of scholars attending the one-year MSc direction, "Fundamental Fields and Forces" at Imperial university. The publication is anxious totally with arithmetic right, even if the emphasis and distinctive issues were selected considering the way differential geometry is utilized to fashionable theoretical physics. This comprises not just the conventional zone of normal relativity but in addition the speculation of Yang-Mills fields, nonlinear sigma types and different kinds of nonlinear box platforms that function in sleek quantum box thought. This variation of the textual content includes an extra bankruptcy that introduces the various uncomplicated principles of normal topology wanted in differential geometry. a few small corrections and additions have additionally been made. the quantity is split into 4 elements. the 1st offers an advent to normal topology, the second one covers introductory co-ordinate-free differential geometry, the 3rd examines geometrical features of the speculation of Lie teams and Lie workforce activities on manifolds, and the fourth offers an advent to the speculation of fibre bundles. within the creation to differential geometry the writer lays huge pressure at the simple rules of "tangent area structure", which he develops from a number of assorted issues of view - a few geometrical, others extra algebraic