Homotopy theory | Algebraic topology
In stable homotopy theory, a branch of mathematics, the sphere spectrum S is the monoidal unit in the category of spectra. It is the suspension spectrum of S0, i.e., a set of two points. Explicitly, the nth space in the sphere spectrum is the n-dimensional sphere Sn, and the structure maps from the suspension of Sn to Sn+1 are the canonical homeomorphisms. The k-th homotopy group of a sphere spectrum is the k-th stable homotopy group of spheres. The localization of the sphere spectrum at a prime number p is called the local sphere at p and is denoted by . (Wikipedia).
From playlist Drawing a sphere
Learn how to determine the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the surface area of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Given the circumference how do you find the surface area of a hemisphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Finding the volume and the surface area of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
Find the volume of a sphere given the circumference
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the volume of a sphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
How do you find the volume of a hemisphere
👉 Learn how to find the volume and the surface area of a sphere. A sphere is a perfectly round 3-dimensional object. It is an object with the shape of a round ball. The distance from the center of a sphere to any point on its surface is called the radius of the sphere. A sphere has a unifo
From playlist Volume and Surface Area
A Dyson Sphere is a megastructure that could be built around a star to harness all the solar energy it gives off. In this video we talk about the different kinds of Dyson Spheres, Dyson Clouds and other megastructures that could be built - and how we might even detect them from Earth. ht
From playlist Guide to Space
Stable Homotopy Seminar, 15: Dualizable and invertible spectra
I present the useful fact that spectra are generated by finite complexes under filtered homotopy colimits. I then define Spanier-Whitehead duality, which is a special case of a notion of duality that exists in any closed symmetric monoidal category. Two natural classes of spectra rise from
From playlist Stable Homotopy Seminar
Higher Algebra 12: The Tate construction
In this video we introduce the Tate construction and especially Tate spectra. This is defined as the cofibre of a certain norm map, which we introduced for completely general group objects and stable infinity categories. We then also explain what it has to do with Poncaré duality and that
From playlist Higher Algebra
Stable Homotopy Seminar, 6: Homotopy Groups of Spectra (D. Zack Garza)
In this episode, D. Zack Garza gives an overview of stable homotopy theory and the types of problems it was designed to solve. He defines the homotopy groups of a spectrum and computes them in the fundamental case of an Eilenberg-MacLane spectrum. ~~~~~~~~~~~~~~~~======================~~~
From playlist Stable Homotopy Seminar
Connections between classical and motivic stable homotopy theory - Marc Levine
Marc Levine March 13, 2015 Workshop on Chow groups, motives and derived categories More videos on http://video.ias.edu
From playlist Mathematics
Stable Homotopy Seminar, 3: The homotopy category of spectra
We discuss the Brown representability theorem, and give the Boardman-Vogt definition of the homotopy category of spectra. Examples include suspension spectra, Omega-spectra arising from cohomology theories, and Thom spectra. ~~~~~~~~~~~~~~~~======================~~~~~~~~~~~~~~~ This is
From playlist Stable Homotopy Seminar
Spectral characterizations of Besse and Zoll Reeb flows - Marco Mazzucchelli
IAS/PU-Montreal-Tel-Aviv Symplectic Geometry Seminar Topic: Spectral characterizations of Besse and Zoll Reeb flows Speaker: Marco Mazzucchelli Affiliation: École normale supérieure de Lyon Date: May 8, 2020 For more video please visit http://video.ias.edu
From playlist Mathematics
Marc Levine: The rational motivic sphere spectrum and motivic Serre finiteness
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist SPECIAL 7th European congress of Mathematics Berlin 2016.
Higher Algebra 11: p-adic completion (corrected)
In this video we introduce the notion of p-adic completion and p-adic equivalence of spectra. We characterize those notions in concrete terms and give examples. Finally we cover the Hasse-square, which can be used to recover X from it completions and its rationalisation. All the material i
From playlist Higher Algebra
Stefan Schwede: Equivariant stable homotopy - Lecture 2
I will use the orthogonal spectrum model to introduce the tensor triangulated category of genuine G-spectra, for compact Lie groups G. I will explain structural properties such as the smash product of G-spectra, and functors relating the categories for varying G (fixed points, geometric fi
From playlist Summer School: Spectral methods in algebra, geometry, and topology
Stable Homotopy Seminar, 16: The Whitehead, Hurewicz, Universal Coefficient, and Künneth Theorems
These are some generalizations of facts from unstable algebraic topology that are useful for calculating in the category of spectra. The Whitehead and Hurewicz theorems say that a map of connective spectra that's a homology isomorphism is a weak equivalence, and that the lowest nonzero hom
From playlist Stable Homotopy Seminar
Link: https://www.geogebra.org/m/D4hmNy9M
From playlist 3D: Dynamic Interactives!