Titlebook: An Introduction to Differential Manifolds; Jacques Lafontaine Textbook 2015 Springer International Publishing Switzerland 2015 De Rham Coh

Grating

Differential Forms,ith what we call line integrals, which is to say the circulation of a vector field . along a curve. This is classically defined as the integral . Here, . is a curve parametrization (in fact a piece of the parametrization as we restricted the parameter to the interval [., .]) and . is an inner produc

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,The Euler-Poincaré Characteristic and the Gauss-Bonnet Theorem,ndex of singular points of vector fields) and Riemannian geometry. We do not have the space to illustrate all of these ideas in detail. To keep with the spirit of the book, the proofs we give will use differential geometry to the greatest extent possible. We nonetheless believe it would be interesti

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