Theorems in homotopy theory

Whitehead theorem

In homotopy theory (a branch of mathematics), the Whitehead theorem states that if a continuous mapping f between CW complexes X and Y induces isomorphisms on all homotopy groups, then f is a homotopy equivalence. This result was proved by J. H. C. Whitehead in two landmark papers from 1949, and provides a justification for working with the concept of a CW complex that he introduced there. It is a model result of algebraic topology, in which the behavior of certain algebraic invariants (in this case, homotopy groups) determines a topological property of a mapping. (Wikipedia).

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Calculus 5.3 The Fundamental Theorem of Calculus

My notes are available at http://asherbroberts.com/ (so you can write along with me). Calculus: Early Transcendentals 8th Edition by James Stewart

From playlist Calculus

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Calculus - The Fundamental Theorem, Part 1

The Fundamental Theorem of Calculus. First video in a short series on the topic. The theorem is stated and two simple examples are worked.

From playlist Calculus - The Fundamental Theorem of Calculus

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Evaluate the integral with e as the lower bound

👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct

From playlist Evaluate Using The Second Fundamental Theorem of Calculus

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Differential Equations | Abel's Theorem

We present Abel's Theorem with a proof. http://www.michael-penn.net

From playlist Differential Equations

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The Second Fundamental Theorem of Calculus

This video introduces and provides some examples of how to apply the Second Fundamental Theorem of Calculus. Site: http://mathispower4u.com

From playlist The Second Fundamental Theorem of Calculus

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Learn to evaluate the integral with functions as bounds

👉 Learn about the fundamental theorem of calculus. The fundamental theorem of calculus is a theorem that connects the concept of differentiation with the concept of integration. The theorem is basically saying that the differentiation of the integral of a function yields the original funct

From playlist Evaluate Using The Second Fundamental Theorem of Calculus

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The Divergence Theorem

Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,

From playlist Vector Calculus

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Multivariable Calculus | The Squeeze Theorem

We calculate a limit using a multivariable version of the squeeze theorem. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist Multivariable Calculus

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Lie Algebras and Homotopy Theory - Jacob Lurie

Members' Seminar Topic: Lie Algebras and Homotopy Theory Speaker: Jacob Lurie Affiliation: Professor, School of Mathematics Date: November 11, 2019 For more video please visit http://video.ias.edu

From playlist Mathematics

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Discrete groups in complex hyperbolic geometry (Lecture - 2) by Pierre Will

Geometry, Groups and Dynamics (GGD) - 2017 DATE: 06 November 2017 to 24 November 2017 VENUE: Ramanujan Lecture Hall, ICTS, Bengaluru The program focuses on geometry, dynamical systems and group actions. Topics are chosen to cover the modern aspects of these areas in which research has b

From playlist Geometry, Groups and Dynamics (GGD) - 2017

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Christoph Winges: On the isomorphism conjecture for Waldhausen's algebraic K-theory of spaces

The lecture was held within the framework of the (Junior) Hausdorff Trimester Program Topology: "The Farrell-Jones conjecture" I will survey recent progress on the isomorphism conjecture for Waldhausen's "algebraic K-theory of spaces" functor, and how this relates to the original isomorp

From playlist HIM Lectures: Junior Trimester Program "Topology"

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Why it took 379 pages to prove 1+1=2

Sign up to Brilliant to receive a 20% discount with this link! https://brilliant.org/upandatom/ Hi! I'm Jade. If you'd like to consider supporting Up and Atom, head over to my Patreon page :) https://www.patreon.com/upandatom Visit the Up and Atom store https://store.nebula.app/collecti

From playlist Math

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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"

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Karen Vogtmann - On the cohomological dimension of automorphism groups of RAAGs

The class of right-angled Artin groups (RAAGs) includes free groups and free abelian groups, Both of these have extremely interesting automorphism groups, which share some properties and not others. We are interested in automorphism groups of general RAAGs, and in particular

From playlist Groupes, géométrie et analyse : conférence en l'honneur des 60 ans d'Alain Valette

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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

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Calculus - The Fundamental Theorem, Part 3

The Fundamental Theorem of Calculus. Specific examples of simple functions, and how the antiderivative of these functions relates to the area under the graph.

From playlist Calculus - The Fundamental Theorem of Calculus

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Atiyah Duality by Samik Basu

PROGRAM DUALITIES IN TOPOLOGY AND ALGEBRA (ONLINE) ORGANIZERS: Samik Basu (ISI Kolkata, India), Anita Naolekar (ISI Bangalore, India) and Rekha Santhanam (IIT Mumbai, India) DATE & TIME: 01 February 2021 to 13 February 2021 VENUE: Online Duality phenomena are ubiquitous in mathematics

From playlist Dualities in Topology and Algebra (Online)

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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

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Stable Homotopy Seminar, 1: Introduction and Motivation

We describe some features that the category of spectra is expected to have, and some ideas from topology it's expected to generalize. Along the way, we review the Freudenthal suspension theorem, and the definition of a generalized cohomology theory. ~~~~~~~~~~~~~~~~======================

From playlist Stable Homotopy Seminar

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The Campbell-Baker-Hausdorff and Dynkin formula and its finite nature

In this video explain, implement and numerically validate all the nice formulas popping up from math behind the theorem of Campbell, Baker, Hausdorff and Dynkin, usually a.k.a. Baker-Campbell-Hausdorff formula. Here's the TeX and python code: https://gist.github.com/Nikolaj-K/8e9a345e4c932

From playlist Algebra

Related pages

CW complex | Compact space | Fundamental group | Künneth theorem | Model category | Real projective space | Topological space | Group homomorphism | Hurewicz theorem | Mathematics | Singular homology | Homotopy group | Homotopy theory | Cyclic group | Shape theory (mathematics) | Isomorphism | Algebraic topology