Maps of manifolds
In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they shed (Wikipedia).
In mathematics, more specifically in differential geometry and topology, various types of functions between manifolds are studied, both as objects in their own right and for the light they shed (Wikipedia).
Today, we take a look at atlases, provide an example for the circle, and discuss different types of atlases we may wish to have on our manifold.
From playlist Manifolds
Today, we take a look at charts, their transition maps, and coordinate functions.
From playlist Manifolds
Manifolds 1.3 : More Examples (Animation Included)
In this video, I introduce the manifolds of product manifolds, tori/the torus, real vectorspaces, matrices, and linear map spaces. This video uses a math animation for visualization. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/5koj5
From playlist Manifolds
Manifolds 2.2 : Examples and the Smooth Manifold Chart Lemma
In this video, I introduce examples of smooth manifolds, such as spheres, graphs of smooth functions, real vectorspaces, linear map spaces, and the Grassmannian of real vectorspaces (G_k(V)). Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Play
From playlist Manifolds
Manifolds 1.2 : Examples of Manifolds
In this video, I describe basic examples of manifolds. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : http://docdro.id/IZO0G25
From playlist Manifolds
Manifolds - Part 16 - Smooth Maps (Definition)
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From playlist Manifolds
Manifolds 2.3 : Smooth Maps and Diffeomorphisms
In this video, I introduce examples and properties of smooth maps, and show the invariance theorems for diffeomorphisms. Email : fematikaqna@gmail.com Code : https://github.com/Fematika/Animations Notes : None yet Playlist :
From playlist Manifolds
Manifolds #5: Tangent Space (part 1)
Today, we introduce the notion of tangent vectors and the tangent vector space at a point on a manifold.
From playlist Manifolds
Prerequisites III: Manifolds & Fiber Bundles - Maurice Weiler
Video recording of the First Italian Summer School on Geometric Deep Learning, which took place in July 2022 in Pescara. Slides: https://www.sci.unich.it/geodeep2022/slides/Manifolds_and_Fiber_Bundles.pdf
From playlist First Italian School on Geometric Deep Learning - Pescara 2022
Manifolds #4: Differentiability
Today, we take a look at a look at how to define the differentiability of a function involving a manifold. This will allow us to define the notion of a tangent vector space in the following video.
From playlist Manifolds
Jintian Zhu - Incompressible hypersurface, positive scalar curvature and positive mass theorem
In this talk, I will introduce a positive mass theorem for asymptotically flat manifolds with fibers (like ALF and ALG manifolds) under an additional but necessary incompressible condition. I will also make a discussion on its connection with surgery theory as well as quasi-local mass and
From playlist Not Only Scalar Curvature Seminar
Johannes Ebert - Rigidity theorems for the diffeomorphism action on spaces of metrics of (...)
The diffeomorphism group $\mathrm{Diff}(M)$ of a closed manifold acts on the space $\mathcal{R}^+ (M)$ of positive scalar curvature metrics. For a basepoint $g$, we obtain an orbit map $\sigma_g: \mathrm{Diff}(M) \to \mathcal{R}^ (M)$ which induces a map $(\sigma_g)_*:\pi_*( \mathrm{Diff}(
From playlist Not Only Scalar Curvature Seminar
What is a Manifold? Lesson 8: Diffeomorphisms
What is a Manifold? Lesson 8: Diffeomorphisms
From playlist What is a Manifold?
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined
Lie Groups and Lie Algebras: Lesson 13 - Continuous Groups defined In this lecture we define a "continuous groups" and show the connection between the algebraic properties of a group with topological properties. Please consider supporting this channel via Patreon: https://www.patreon.co
From playlist Lie Groups and Lie Algebras
Christoph Winges: Automorphisms of manifolds and the Farrell Jones conjectures
The lecture was held within the framework of the Hausdorff Trimester Program: K-Theory and Related Fields. Building on previous work of Bartels, Lück, Reich and others studying the algebraic K-theory and L-theory of discrete group rings, the validity of the Farrell-Jones Conjecture has be
From playlist HIM Lectures: Trimester Program "K-Theory and Related Fields"
What is General Relativity? Special Lecture: Tangent Spaces and Coordinate Basis
What is General Relativity? Special Lecture: Tangent Spaces and Coordinate Basis This is a LONG lecture covering a narrow but important topic: tangent spaces and the coordinate basis. It is intended for anyone who has trouble understanding why a manifold has a vector space at every point
From playlist What is a Manifold?
Isocontact and isosymplectic immersions and embeddings by Mahuya Datta
J-Holomorphic Curves and Gromov-Witten Invariants DATE:25 December 2017 to 04 January 2018 VENUE:Madhava Lecture Hall, ICTS, Bangalore Holomorphic curves are a central object of study in complex algebraic geometry. Such curves are meaningful even when the target has an almost complex stru
From playlist J-Holomorphic Curves and Gromov-Witten Invariants
