This is the second volume of a three-volume introduction to modern geometry, with emphasis on applications to other areas of mathematics and theoretical physics. Topics covered include homotopy groups, fibre bundles, dynamical systems, and foliations. The exposition is simple and concrete, and in a terminology palatable to physicists.
Examples of Manifolds
Foundational Questions. Essential Facts Concerning Functions on a Manifold. Typical Smooth Mappings
The Degree of a Mapping. The Intersection Index of Submanifolds.
Orientability of Manifolds. The Fundamental Group. Covering Spaces (Fibre Bundles with Discrete Fibre)
Smooth Fibre Bundles
Some Examples of Dynamical Systems and Foliations on Manifolds
The Global Structure of Solutions of Higher-Dimensional Variational Problems