Because the occasions of Gauss, Riemann, and Poincaré, one of many primary ambitions of the research of manifolds has been to narrate neighborhood analytic homes of a manifold with its worldwide topological homes. one of the excessive issues in this direction are the Gauss-Bonnet formulation, the de Rham advanced, and the Hodge theorem; those effects exhibit, specifically, that the significant device in achieving the most target of world research is the speculation of differential kinds.
The ebook via Morita is a accomplished creation to differential types. It starts off with a brief advent to the concept of differentiable manifolds after which develops uncomplicated houses of differential varieties in addition to primary effects relating them, corresponding to the de Rham and Frobenius theorems. the second one half the ebook is dedicated to extra complex fabric, together with Laplacians and harmonic types on manifolds, the techniques of vector bundles and fiber bundles, and the idea of attribute periods. one of the much less conventional themes handled is a close description of the Chern-Weil concept.
The e-book can function a textbook for undergraduate scholars and for graduate scholars in geometry.
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