After a line, a circle is the simplest example of a topological manifold. Topology ignores bending, so a small piece … See more

Informally, a manifold is a space that is "modeled on" Euclidean space.
There are many different kinds of manifolds. In geometry and topology, all manifolds are topological manifolds, possibly wit… See more

The spherical Earth is navigated using flat maps or charts, collected in an atlas. Similarly, a manifold can be described using mathematical maps, called coordinate charts, collected in a mathematical atlas. It is not gene… See more

A manifold with boundary is a manifold with an edge. For example, a sheet of paper is a 2-manifold with a 1-dimensional boundary. The boundary of an -manifold with boundary is an -manifold. A disk (circle plus interior) is a 2-manifol… See more

A single manifold can be constructed in different ways, each stressing a different aspect of the manifold, thereby leading to a slightly different viewpoint.
Perhaps the simplest way to construct a manifold is … See more

The study of manifolds combines many important areas of mathematics: it generalizes concepts such as curves and surfaces as well as ideas from linear algebra and topology.
Before the … See more

The simplest kind of manifold to define is the topological manifold, which looks locally like some "ordinary" Euclidean space . By definition, all manifolds are topological manifolds, so the phrase "topological manifold" i… See more