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If (X,x) and (Y,y) are pointed spaces, a pointed map is a continuous map F:X->Y with the additional requirement that F(x)=y.

A knot obtained from a tangle which can be represented by a finite sequence of integers.

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 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.

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.

A tree of links obtained by repeatedly choosing a crossing, applying the skein relationship to obtain two simpler links, and repeating the process. The tree depth of a ...

A manifold possessing a metric tensor. For a complete Riemannian manifold, the metric d(x,y) is defined as the length of the shortest curve (geodesic) between x and y. Every ...

Suppose for every point x in a manifold M, an inner product <·,·>_x is defined on a tangent space T_xM of M at x. Then the collection of all these inner products is called ...