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

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

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.

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s80 Pages
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An Introduction to   Differential Topology, de Rham Theory and Morse Theory

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.

s80 Pages
Introduction   to Differential Topology by Uwe Kaiser

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.

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Introduction To Differential Topology

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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.

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Combinatorial Differential     Topology and Geometry (PDF 30p)

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