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Skip to search form Skip to main content You are currently offline. Some features of the site may not work correctly. DOI: Introduction 2. The alternating algebra 3. De Rham cohomology 4. Chain complexes and their cohomology 5. The Mayer-Vietoris sequence 6. Homotopy 7. Applications of De Rham cohomology 8. Smooth manifolds 9. Differential forms on smooth manifolds Integration on manifolds Degree, linking numbers and index of vector fields The Poincare-Hopf theorem Poincare duality The complex projective space CPn Fiber bundles and vector bundles View PDF.
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From Calculus to Cohomology: De Rham Cohomology and Characteristic Classes
If you are a seller for this product, would you like to suggest updates through seller support? Have one to sell? Sell yours here. Currently unavailable. We don't know when or if this item will be back in stock. Review ' It treats de Rham cohomology in an intellectually rigourous yet accessible manner which makes it ideal for a beginning graduate student.
From Calculus to Cohomology : De Rham Cohomology and Characteristic Classes
De Rham cohomology is the cohomology of differential forms. This book offers a self-contained exposition to this subject and to the theory of characteristic classes from the curvature point of view. It requires no prior knowledge of the concepts of algebraic topology or cohomology. The first ten chapters study cohomology of open sets in Euclidean space, treat smooth manifolds and their cohomology and end with integration on manifolds. The text includes over exercises, and gives the background necessary for the modern developments in gauge theory and geometry in four dimensions, but it also serves as an introductory course in algebraic topology.