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A knot used to shorten a long rope.

A relationship between knot polynomials for links in different orientations (denoted below as L_+, L_0, and L_-). J. H. Conway was the first to realize that the Alexander ...

The Reidemeister move of type III.

If M^n is a differentiable homotopy sphere of dimension n>=5, then M^n is homeomorphic to S^n. In fact, M^n is diffeomorphic to a manifold obtained by gluing together the ...

The space join of a topological space X and a point P, C(X)=X*P.

A space which is isomorphic to a Borel subset B of a Polish space equipped with its sigma-algebra of Borel sets.

A set that is a smooth embedded two-dimensional manifold except for a subset that consists of smooth embedded curves, except for a set of isolated points.

An ordinary knot in three dimensions suspended in four dimensions to create a knotted 2-sphere. Suspended knots are not smooth at the poles.

A pair (M,omega), where M is a manifold and omega is a symplectic form on M. The phase space R^(2n)=R^n×R^n is a symplectic manifold. Near every point on a symplectic ...

For any two points x,y in X, there is an open set U such that x in U and y not in U or y in U and x not in U. A space fulfilling this axiom is called a T0-space.