Properties of topological spaces | Algebraic topology
In topology, a branch of mathematics, a topological space X is said to be simply connected at infinity if for any compact subset C of X, there is a compact set D in X containing C so that the induced map is the zero map. Intuitively, this is the property that loops far away from a small subspace of X can be collapsed, no matter how bad the small subspace is. The Whitehead manifold is an example of a 3-manifold that is contractible but not simply connected at infinity. Since this property is invariant under homeomorphism, this proves that the Whitehead manifold is not homeomorphic to R3. However, it is a theorem of John R. Stallings that for , a contractible n-manifold is homeomorphic to Rn precisely when it is simply connected at infinity. (Wikipedia).
This video provides a description of infinity with several examples. http://mathispower4u.com
From playlist Linear Inequalities in One Variable Solving Linear Inequalities
Touching Infinity: It's Not Out of Reach
The conventional way to represent the Real Number system is to think of the numbers as corresponding to points along an infinite straight line. The problem is that in this representation there is no place for "infinity". Infinity is not a real number. This video shows an alternate visua
From playlist Lessons of Interest on Assorted Topics
Definition of infinity In this video, I define the concept of infinity (as used in analysis), and explain what it means for sup(S) to be infinity. In particular, the least upper bound property becomes very elegant to write down. Check out my real numbers playlist: https://www.youtube.co
From playlist Real Numbers
What’s the biggest number you can think of? Well, what about one more than that number? We can’t really comprehend the idea of infinity, but it’s still a useful concept in science. Brian Greene explains more. Subscribe to our YouTube Channel for all the latest from World Science U. Visit
From playlist Science Unplugged: Physics
How many kinds of infinity are there?
A lot. List with links: http://vihart.com/how-many-kinds-of-infinity-are-there/
From playlist Doodling in Math and more | Math for fun and glory | Khan Academy
How to visualize infinity in concrete terms.
From playlist Summer of Math Exposition 2 videos
Can You Define the Immeasurable?
What is infinity? Can you define something that, by definition, has no boundaries? A subject extensively studied by philosophers, mathematicians, and more recently, physicists and cosmologists, infinity still stands as an enigma of the intellectual world. We asked people from all walks of
From playlist Mathematics
It's a concept which intrigues mathematicians, but scientists aren't so keen on it. More at http://www.sixtysymbols.com/
From playlist From Sixty Symbols
There are just as many numbers between 0 and 1 as there are between 0 and 2. Though infinity may behave counterintuitively at first, everything makes more sense as we reexamine the topic from the basics. Created by: Cory Chang Produced by: Vivian Liu Script Editors: Justin Chen, Brandon C
From playlist Infinity, and Beyond!
In this video, we introduce and discuss spectra (in the sense of homotopy theory). We explain how they generalise abelian groups. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further informa
From playlist Higher Algebra
Anna Miriam Benini: Polynomial versus transcendental dynamics
HYBRID EVENT Recorded during the meeting "Advancing Bridges in Complex Dynamics" the September 24, 2021 by the Centre International de Rencontres Mathématiques (Marseille, France) Filmmaker: Guillaume Hennenfent Find this video and other talks given by worldwide mathematicians on CIRM
From playlist Dynamical Systems and Ordinary Differential Equations
Lecture 8: Bökstedt Periodicity
In this video, we give a proof of Bökstedts fundamental result showing that THH of F_p is polynomial in a degree 2 class. This will rely on unlocking its relation to the dual Steenrod algebra and the fundamental fact, that the latter is free as an E_2-Algebra. Feel free to post comments a
From playlist Topological Cyclic Homology
Cherkis 2021 04 05Yang-Mills Instantons, Quivers and Bows - Sergey Cherkis
Analysis Seminar Topic: Yang-Mills Instantons, Quivers and Bows Speaker: Sergey Cherkis Affiliation: University of Arizona; Member, School of Mathematics Date: April 05, 2021 For more video please visit http://video.ias.edu
From playlist Mathematics
J. Wang - Topological rigidity and positive scalar curvature
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Developments in 4-manifold topology arising from a theorem of Donaldson's - John Morgan [2017]
slides for this talk: https://drive.google.com/file/d/1_wHviPab9klzwE4UkCOvVecyopxDsZA3/view?usp=sharing Name: John Morgan Event: Workshop: Geometry of Manifolds Event URL: view webpage Title: Developments in 4-manifold topology arising from a theorem of Donaldson's Date: 2017-10-23 @9:3
From playlist Mathematics
Lecture 17: Frobenius lifts and group rings
In this video, we "compute" TC of spherical group rings and more generally cyclotomic spectra with Frobenius lifts. Feel free to post comments and questions at our public forum at https://www.uni-muenster.de/TopologyQA/index.php?qa=tc-lecture Homepage with further information: https://
From playlist Topological Cyclic Homology
Lecture 11: Negative Topological cyclic homology
Correction: In the definition of stable ∞-categories at the very beginning, we forgot the condition that C has a zero object, i.e. the initial and terminal objects agree via the canonical morphism between them. Sorry for the confusion! In this video we define negative topological cyclic h
From playlist Topological Cyclic Homology
J. Wang - Topological rigidity and positive scalar curvature (version temporaire)
In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with positive scalar curvature is homeomorphic to the Euclidean 3-space. We will furthermore explain the
From playlist Ecole d'été 2021 - Curvature Constraints and Spaces of Metrics
Introduction to Limits at Infinity (Part 1)
This video introduces limits at infinity. https://mathispower4u.com
From playlist Limits at Infinity and Special Limits
Lecture 10: The circle action on THH
In this video we construct an action of the circle group S^1 = U(1) on the spectrum THH(R). We will see how this is the homotopical generalisation of the Connes operator. The key tool will be Connes' cyclic category. The speaker is of course Achim Krause and not Thomas Nikolaus as falsely
From playlist Topological Cyclic Homology