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A Möbius strip with finite thickness.

A knot having the property that no surgery could possibly yield a counterexample to the Poincaré conjecture is said to satisfy Property P (Adams 1994, p. 262).

A Euclidean-like space having line element ds^2=(dz^1)^2+...+(dz^p)^2-(dz^(p+1))^2-...-(dz^(p+q))^2, having dimension m=p+q (Rosen 1965). In contrast, the signs would be all ...

A pseudo-Riemannian manifold is a manifold which has a metric that is of the signature diag(-,+,...,+), as compared to a Riemannian manifold, which has a signature of all ...

A surface constructed by placing a family of figure-eight curves into R^3 such that the first and last curves reduce to points. The surface has parametric equations x(u,v) = ...

A real vector space is a vector space whose field of scalars is the field of reals. A linear transformation between real vector spaces is given by a matrix with real entries ...

A knot diagram in which none of the crossings are reducible.

The Reeb foliation of the hypersphere S^3 is a foliation constructed as the union of two solid tori with common boundary.

The equivalence of manifolds under continuous deformation within the embedding space. Knots of opposite chirality have ambient isotopy, but not regular isotopy.

Two links can be continuously deformed into each other iff any diagram of one can be transformed into a diagram of the other by a sequence of Reidemeister moves.