Search results
Results from the WOW.Com Content Network
In mathematics, a 3-manifold is a topological space that locally looks like a three-dimensional Euclidean space. A 3-manifold can be thought of as a possible shape of the universe. Just as a sphere looks like a plane (a tangent plane) to a small and close enough observer, all 3-manifolds look like our universe does to a small enough observer ...
Manifolds need not be closed; thus a line segment without its end points is a manifold. They are never countable, unless the dimension of the manifold is 0. Putting these freedoms together, other examples of manifolds are a parabola, a hyperbola, and the locus of points on a cubic curve y 2 = x 3 − x (a closed loop piece and an open, infinite ...
If is a prime 3-manifold then either it is or the non-orientable bundle over , or it is irreducible, which means that any embedded 2-sphere bounds a ball. So the theorem can be restated to say that there is a unique connected sum decomposition into irreducible 3-manifolds and fiber bundles of S 2 {\displaystyle S^{2}} over S 1 . {\displaystyle ...
Introduction to 3-Manifolds is a mathematics book on low-dimensional topology. It was written by Jennifer Schultens and published by the American Mathematical Society in 2014 as volume 151 of their book series Graduate Studies in Mathematics.
In mathematics, a spherical 3-manifold M is a 3-manifold of the form = / where is a finite subgroup of O(4) acting freely by rotations on the 3-sphere. All such manifolds are prime, orientable, and closed. Spherical 3-manifolds are sometimes called elliptic 3-manifolds.
In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, ... Similarly for 3-manifolds: of the 8 geometries ...
Once a small subfield of geometric topology, the theory of 3-manifolds has experienced tremendous growth in the latter half of the 20th century. The methods used tend to be quite specific to three dimensions, since different phenomena occur for 4-manifolds and higher dimensions.
Peter Orlik, Seifert manifolds, Lecture Notes in Mathematics 291, Springer (1972). Frank Raymond, Classification of the actions of the circle on 3-manifolds, Transactions of the American Mathematical Society 31, (1968) 51–87. William H. Jaco, Lectures on 3-manifold topology ISBN 0-8218-1693-4