Structures on manifolds | Manifolds

Analytic manifold

In mathematics, an analytic manifold, also known as a manifold, is a differentiable manifold with analytic transition maps. The term usually refers to real analytic manifolds, although complex manifolds are also analytic. In algebraic geometry, analytic spaces are a generalization of analytic manifolds such that singularities are permitted. For , the space of analytic functions, , consists of infinitely differentiable functions , such that the Taylor series converges to in a neighborhood of , for all . The requirement that the transition maps be analytic is significantly more restrictive than that they be infinitely differentiable; the analytic manifolds are a proper subset of the smooth, i.e. , manifolds. There are many similarities between the theory of analytic and smooth manifolds, but a critical difference is that analytic manifolds do not admit analytic partitions of unity, whereas smooth partitions of unity are an essential tool in the study of smooth manifolds. A fuller description of the definitions and general theory can be found at differentiable manifolds, for the real case, and at complex manifolds, for the complex case. (Wikipedia).

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From playlist Course 8: Complex Analysis

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From playlist Analytic and Algebraic Geometry-2018

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From playlist Mathematics

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From playlist Analytic and Algebraic Geometry-2018

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From playlist Analytic and Algebraic Geometry-2018

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From playlist Analytic and Algebraic Geometry-2018

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From playlist Analytic and Algebraic Geometry-2018

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From playlist Analytic and Algebraic Geometry-2018

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From playlist Mathematics

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Pierre Albin : Extending the Cheeger-Müller theorem through degeneration

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From playlist Topology

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Rahim Moosa: Nonstandard compact complex manifolds with a generic auto-morphism

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From playlist Higgs Bundles

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From playlist Ecole d'été 2019 - Foliations and algebraic geometry

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On the geometry and topology of zero sets of Schrödinger eigenfunctions - Yaiza Canzani

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From playlist Mathematics

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Pierre Albin: The sub-Riemannian limit of a contact manifold

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From playlist Global Noncommutative Geometry Seminar (Americas)

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From playlist Mathematics

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From playlist Mathematics

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From playlist Analytic and Algebraic Geometry-2018

Related pages

Analytic function | Mathematics | Analytic space | Smoothness | Partition of unity | Complex manifold | Differentiable manifold