In topology, a branch of mathematics, a prime manifold is an n-manifold that cannot be expressed as a non-trivial connected sum of two n-manifolds. Non-trivial means that neither of the two is an n-sphere.A similar notion is that of an irreducible n-manifold, which is one in which any embedded (n − 1)-sphere bounds an embedded n-ball. Implicit in this definition is the use of a suitable category, such as the category of differentiable manifolds or the category of piecewise-linear manifolds. The notions of irreducibility in algebra and manifold theory are related. An irreducible manifold is prime, although the converse does not hold. From an algebraist's perspective, prime manifolds should be called "irreducible"; however the topologist (in particular the 3-manifold topologist) finds the definition above more useful. The only compact, connected 3-manifolds that are prime but not irreducible are the trivial 2-sphere bundle over the circle S1 and the twisted 2-sphere bundle over S1. According to a theorem of Hellmuth Kneser and John Milnor, every compact, orientable 3-manifold is the connected sum of a unique (up to homeomorphism) collection of prime 3-manifolds. (Wikipedia).
Prime Numbers and their Mysterious Distribution (Prime Number Theorem)
Primes are the building blocks of math. But just how mysterious are they? Our study of prime numbers dates back to the ancient Greeks who first recognized that certain numbers can't be turned into rectangles, or that they can't be factored into any way. Over the years prime numbers have
From playlist Prime Numbers
The Prime Number Theorem, an introduction ← Number Theory
An introduction to the meaning and history of the prime number theorem - a fundamental result from analytic number theory. Narrated by Cissy Jones Artwork by Kim Parkhurst, Katrina de Dios and Olga Reukova Written & Produced by Michael Harrison & Kimberly Hatch Harrison ♦♦♦♦♦♦♦♦♦♦ Ways t
From playlist Number Theory
Algebra - Ch. 6: Factoring (4 of 55) What is a Prime Number?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a prime number. A prime number is a positive integer that can only be written as a product of one and itself. Its factors are “1” and itself. To donate: http://www.ilectureonline.com/
From playlist ALGEBRA CH 6 FACTORING
An easy intro to prime numbers and composite numbers that MAKES SENSE. What are prime numbers? A prime number is a number that has exactly 2 factors: two and itself. What are composite numbers? A composite number is one which has two or more factors. What is the difference between a p
From playlist Indicies (Exponents) and Primes
In this video, we explore the "pattern" to prime numbers. I go over the Euler product formula, the prime number theorem and the connection between the Riemann zeta function and primes. Here's a video on a similar topic by Numberphile if you're interested: https://youtu.be/uvMGZb0Suyc The
From playlist Other Math Videos
Prime Gaps and The Crazy Sequences of Steps
When we try to avoid multiples of numbers using sequences we find a very unique way to create a prime list that has its own properties and curiosities. These sequences are state machines that can become very complex to generate but should be very simple to read.
From playlist Summer of Math Exposition Youtube Videos
Interesting Facts About the Last Digits of Prime Numbers
This video explains some interesting facts about the last digits of prime numbers.
From playlist Mathematics General Interest
1,010,010,101,000,011 - #MegaFavNumbers
This is my submission to the #megafavnumbers project. My number is 1010010101000011, which is prime in bases 2, 3, 4, 5, 6 and 10. I've open-sourced my code: https://bitbucket.org/Bip901/multibase-primes Clarification: by "ignoring 1" I mean ignoring base 1, since this number cannot be fo
From playlist MegaFavNumbers
Jonathan Rosenberg: Positive scalar curvature on a class of spin pseudomanifolds.
Talk by Jonathan Rosenberg in Global Noncommutative Geometry Seminar (Americas) http://www.math.wustl.edu/~xtang/NCG-Seminar on April 22, 2020.
From playlist Global Noncommutative Geometry Seminar (Americas)
What is a Manifold? Lesson 8: Diffeomorphisms
What is a Manifold? Lesson 8: Diffeomorphisms
From playlist What is a Manifold?
What is General Relativity? Lesson 65: Scalar curvature Part 14
What is General Relativity? Lesson 65: Scalar curvature Part 14 We continue our examination of Section 4.4.6 of "A Simple Introduction to Particle Physics Part II - Geometric Foundations of Relativity." We are pushing to the end of this analysis. In this lesson we work with a coordinate t
From playlist What is General Relativity?
“Closed Geodesics on Surfaces Pt.2” - Nancy Hingston
Nancy Hingston TCNJ “Closed geodesics on surfaces” Wednesday May 18
From playlist Mathematics
Emily Stark: Action rigidity for free products of hyperbolic manifold groups
CIRM VIRTUAL EVENT Recorded during the meeting"Virtual Geometric Group Theory conference " the May 22, 2020 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 Virtual Conference
Contact invariants in sutured monopole and instanton homology - Steven Sivek
Steven Sivek University of Warwick March 5, 2014 Kronheimer and Mrowka recently used monopole Floer homology to define an invariant of sutured manifolds, following work of Juhász in Heegaard Floer homology. In this talk, I will construct an invariant of a contact structure on a 3-manifold
From playlist Mathematics
Prealgebra Lecture 4.2: Prime Factorization and Simplification of Fractions
https://www.patreon.com/ProfessorLeonard Prealgebra Lecture 4.2: Prime Factorization and Simplification of Fractions
From playlist Prealgebra (Full Length Videos)
Hyperbolic Knot Theory (Lecture - 2) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Panorama of Mathematics: Peter Scholze
Panorama of Mathematics To celebrate the tenth year of successful progression of our cluster of excellence we organized the conference "Panorama of Mathematics" from October 21-23, 2015. It outlined new trends, results, and challenges in mathematical sciences. Peter Scholze: "Locally sym
From playlist Panorama of Mathematics
Thomas Koberda - "Residual properties of 3-manifold groups"
Koberda delivers a research level talk at the Worldwide Center of Mathematics.
From playlist Center of Math Research: the Worldwide Lecture Seminar Series
Virtual domination of 3-manifolds - Hongbin Sun
Hongbin Sun, UC Berkeley October 6, 2015 http://www.math.ias.edu/wgso3m/agenda 015-2016 Monday, October 5, 2015 - 08:00 to Friday, October 9, 2015 - 12:00 This workshop is part of the topical program "Geometric Structures on 3-Manifolds" which will take place during the 2015-2016 academi
From playlist Workshop on Geometric Structures on 3-Manifolds
#MegaFavNumbers: Mine is multiple primes at once.
I didn't even find it in the OEIS. The other kind of manifold primes got their entry in the OEIS. Prime in 7 bases: https://oeis.org/A052027 Prime in 8 bases: https://oeis.org/A038537 Prime in all 9 Bases: https://oeis.org/A084482 Special thanks to caplja1 He provided the python-code
From playlist MegaFavNumbers