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An operation that takes two vector bundles over a fixed space and produces a new vector bundle over the same space. If E_1 and E_2 are vector bundles over B, then the Whitney ...

Let a closed surface have genus g. Then the polyhedral formula generalizes to the Poincaré formula chi(g)=V-E+F, (1) where chi(g)=2-2g (2) is the Euler characteristic, ...

A sutured manifold is a tool in geometric topology which was first introduced by David Gabai in order to study taut foliations on 3-manifolds. Roughly, a sutured manifold is ...

An archaic name for topology.

The map which takes points on the surface of a sphere S^2 to their antipodal points.

A topological space X in which each subset of X of the "first category" has an empty interior. A topological space which is homeomorphic to a complete metric space is a Baire ...

A vector field u satisfying the vector identity ux(del xu)=0 where AxB is the cross product and del xA is the curl is said to be a Beltrami field.

The direct limit of the cohomology groups with coefficients in an Abelian group of certain coverings of a topological space.

A cellular space is a T2-space that has the structure of a so-called CW-complex.

Two open manifolds M and M^' are cobordant if there exists a manifold with boundary W^(n+1) such that an acceptable restrictive relationship holds.