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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.

The direct product of the rings R_gamma, for gamma some index set I, is the set product_(gamma in I)R_gamma={f:I-> union _(gamma in I)R_gamma|f(gamma) in R_gamma all gamma in ...

Eliminate each knot crossing by connecting each of the strands coming into the crossing to the adjacent strand leaving the crossing. The resulting strands no longer cross but ...

The Reidemeister move of type III.

A graphical partitioning based on the eigenvalues and eigenvectors of the Laplacian matrix of a graph.

A topological sort is a permutation p of the vertices of a graph such that an edge {i,j} implies that i appears before j in p (Skiena 1990, p. 208). Only acyclic digraphs can ...

A projection of a link is tricolorable if each of the strands in the projection can be colored in one of three different colors such that, at each crossing, all three colors ...

Let S be a nonempty set, then an ultrafilter on S is a nonempty collection F of subsets of S having the following properties: 1. emptyset not in F. 2. If A,B in F, then A ...