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A concordance between knots K_0 and K_1 in S^3 is a locally flat cylinder C=S^1×[0,1] embedded in S^3×[0,1] in such a way that the ends S^1×{1} are embedded in S^3×{i} as ...

A topological structure which interpolates between contact structures and codimension-one foliations.

Every compact 3-manifold is the connected sum of a unique collection of prime 3-manifolds.

A continuous vector bundle is a vector bundle pi:E->M with only the structure of a topological manifold. The map pi is continuous. It has no smooth structure or bundle metric.

A sphere with four punctures occurring where a knot passes through the surface.

The cotangent bundle of a manifold is similar to the tangent bundle, except that it is the set (x,f) where x in M and f is a dual vector in the tangent space to x in M. The ...

The slicing of a three-dimensional object by a plane (or more general slice).

A continuum is a decomposable continuum if and only if it is the union of two of its proper subcontinua. A continuum that is not decomposable is an indecomposable continuum.

Two manifolds are said to be diffeomorphic if there exists a diffeomorphism between them.

Disconnectivities are mathematical entities which stand in the way of a space being contractible (i.e., shrunk to a point, where the shrinking takes place inside the space ...