This note covers
the following topics: Smooth manifolds and smooth maps, Tangent spaces and differentials ,
Regular and singular values , Manifolds with boundary, Immersions
and embeddings , Degree mod 2 , Orientation of manifolds and
Applications of degree.
This
note explains the following topics: preliminaries, Different homology theories and their
interaction, Classifying spaces, An introduction to symplectic topology.
This note covers the following topics: Basics of Differentiable
Manifolds, Local structure of smooth maps, Transversality Theory,
IDifferential Forms and de Rham Theory, TIensors and some Riemannian
Geometry.
The
first half of the book deals with degree theory, the Pontryagin construction,
intersection theory, and Lefschetz numbers. The second half of the book is
devoted to differential forms and deRham cohomology.