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Geometry of Differential Forms Shigeyuki Morita
Publisher: American Mathematical Society

Number theory: Serre, A Course in Arithmetic. I have needed to learn differential geometry for a long time. It took me quite a while to find a good explanation of differential forms & I Spivak has a nice quip in Differential Geometry, Vol. Principal theorems and applications of differential. I understand what forms are, and understand their properties in R2 and R3 (exactn. In Calculus is being discussed at Physics Forums. Do Carmo Differential Forms and Applications "This book treats differential forms and uses them to study some local and global aspects of differential geometry of surfaces. I've had a moderate amount of exposure to the study of differential forms in the context of pure differential geometry, as well as in the background of studies in hypercomplex analysis, abstract algebra, etc. So I'm a little stuck on the concept of forms on a manifold. In the context of string theory, in particular when we're dealing with a low energy effective action, if we have an effective action of the form: $$S_{eff} \sim S^{(0)} + \alpha S^{(1)} + (\alpha)^2 S^{(2)} + \ldots$$. Topology: Bott and Tu's Differential Forms in Algebraic Topology is a very readable introduction to smooth manifolds and goes far; everyone should read it. The book treats differential forms and uses them to study some local and global aspects of the differential geometry of surfaces. Integrals of differential forms play a fundamental role in modern differential geometry. This issue; for example, diffeological, differential, and Frölicher structures are defined on arbitrary sets.