differential-geometry

I'm currently reading through Loring Tu's "An Introduction to Manifolds", which I've linked over here. I have a question about proposition 6.10, where Tu proves that every chart $(U, \phi)$ ...

synthetic differential geometry Introductions geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeometry Differentials Tangency The magic algebraic facts Theorems Axiomatics Models smooth algebra (-ring) differential equations, variational calculus Chern-Weil theory, ∞-Chern-Weil theory Cartan geometry (super, higher) Let and be two smooth manifolds of…

See also differentiable function. analysis (differential/integral calculus, functional analysis, topology) metric space, normed vector space open ball, open subset, neighbourhood convergence, limit of a sequence compactness, sequential compactness … … synthetic differential geometry Introductions geometry of physics: coordinate systems, smooth spaces, manifolds, smooth homotopy types, supergeomet…

I would like to share a concise proof of the Poincaré Lemma using the flow of a radial vector field. Theorem (Poincaré Lemma) Assume that a smooth ##k##-form $$\omega = \sum_{i_1 < \dots < i_k} \omega_{i_1 \dots i_k} (x) dx^{i_1} \wedge \dots \wedge dx^{i_k}$$ is defined in a... Read more

Discussion of twisted differential K-theory and its relation to D-brane charge in type II string theory: and for KO: On differential Cohomotopy and Hypothesis H: On locality of extended functorial field theory: On the cobordism hypothesis for extended functorial field theory equipped with geometric structure (such as conformal field theory etc.): On the ordinary differential cohomology and differ…