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An (ordinary) torus is a surface having genus one, and therefore possessing a single "hole" (left figure). The single-holed "ring" torus is known in older literature as an ...

Any link can be represented by a closed braid.

The map H_n(X,A)->H_(n-1)(A) appearing in the long exact sequence of a pair axiom.

That portion of a region lying "outside" a specified boundary.

A property of a space which is also true of each of its subspaces. Being "first-countable" is hereditary, but having a given genus is not.

An open connected set is called a region (sometimes also called a domain).

If the abstract simplicial complex S is isomorphic with the vertex scheme of the simplicial complex K, then K is said to be a geometric realization of S, and is uniquely ...

A half-space is that portion of an n-dimensional space obtained by removing that part lying on one side of an (n-1)-dimensional hyperplane. For example, half a Euclidean ...

Let G be a locally compact Abelian group. Let G^* be the group of all continuous homeomorphisms G->R/Z, in the compact open topology. Then G^* is also a locally compact ...

A Reeb component is a Reeb foliation (M,F) whose leaves are proper. A foliation which has no Reeb components is said to be Reebless.