Introduction to Quantum Mechanics | Category Theory in Context | An Introductory Course on Differentiable Manifolds | An Introduction to Homological Algebra | Introduction to Tensor Analysis and the Calculus of Moving Surfaces | Curvature and Homology | Cohomology Operations And Applications In Homotopy Theory
A self-contained development of cohomological theory constitutes the central part of the book. Topics include categories and functors, the Äech cohomology with coefficients in sheaves, the theory of fiber bundles, and differentiable, foliated, and complex analytic manifolds. The final chapter covers the theorems of de Rham and Dolbeault-Serre and examines the theorem of Allendoerfer and Eells, with applications of these theorems to characteristic classes and the general theory of harmonic forms.
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