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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 
Differential Topology by Andrew Kobin
This note covers Smooth manifolds, Regular values, Transversality and embeddings, Vector bundles.
Author(s): Andrew Kobin
52 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
Introduction to Differential Topology by Uwe Kaiser
This book gives a deeper account of basic ideas of differential topology than usual in introductory texts. Also many more examples of manifolds like matrix groups and Grassmannians are worked out in detail. Topics covered includes: Continuity, compactness and connectedness, Smooth manifolds and maps, Regular values and Sards theorem, Manifolds with boundary and orientations, Smooth homotopy and vector bundles, Intersection numbers, vector fields and Euler characteristic.
Author(s): Uwe Kaiser
110 Pages
Differential topology Lecture notes (PDF 20p)
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.
Author(s): Sergei Tabachnikov
20 Pages