Topics in Differential Topology by Mohammad F Tehrani

Topics in Differential Topology by Mohammad F Tehrani

This note explains the following topics: preliminaries, Different homology theories and their interaction, Classifying spaces, An introduction to symplectic topology.

Author(s): Mohammad F Tehrani

104 Pages

Lectures on differential topology by Alexander Kupers

The contents include: Spheres in Euclidean space, Smooth manifolds, Submanifolds and tori, Smooth maps and their derivatives, Tangent bundles, Immersions and submersions, Quotients and coverings, Three further examples of manifolds, Partitions of unity and the weak Whitney embedding theorem, Transversality and the improved preimage theorem, Stable and generic classes of smooth maps, Transverse maps are generic, Knot theory, Orientations and integral intersection theory, Integration on manifolds, De Rham cohomology, Invariant forms in de Rham cohomology, First fundamental theorem of Morse theory, Second fundamental theorem of Morse theory, Outlook.

Author(s): Alexander Kupers

279 Pages

An Introduction to Differential Topology, de Rham Theory and Morse Theory

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.

Author(s): Michael Muger

80 Pages

Introduction To Differential Topology

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.

Author(s): Joel W. Robbin and Dietmar A. Salamon

306 Pages