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A Reeb component is a Reeb foliation (M,F) whose leaves are proper. A foliation which has no Reeb components is said to be Reebless.

The m×n rook complement graph K_m square K_n^_ is the graph complement of the m×n rook graph. It has vertex count mn and edge count 2(m; 2)(n; 2), where (n; k) is a binomial ...

A transformation in which all points along a given line L remain fixed while other points are shifted parallel to L by a distance proportional to their perpendicular distance ...

The nth-order Sierpiński tetrahedron graph is the connectivity graph of black triangles in the nth iteration of the tetrix fractal. The first three iterations are shown ...

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 ...

A normed vector space X=(X,||·||_X) is said to be uniformly convex if for sequences {x_n}={x_n}_(n=1)^infty, {y_n}={y_n}_(n=1)^infty, the assumptions ||x_n||_X<=1, ...

A theorem that classifies planar regular closed curves up to regular homotopy by their contour winding numbers (Whitney 1937). In his thesis, S. Smale generalized this result ...

If W is a simply connected, compact manifold with a boundary that has two components, M_1 and M_2, such that inclusion of each is a homotopy equivalence, then W is ...

sum_(y=0)^m(-1)^(m-y)q^((m-y; 2))[m; y]_q(1-wq^m)/(q-wq^y) ×(1-wq^y)^m(-(1-z)/(1-wq^y);q)_y=(1-z)^mq^((m; 2)), where [n; y]_q is a q-binomial coefficient.

The cube is the Platonic solid composed of six square faces that meet each other at right angles and has eight vertices and 12 edges. It is also the uniform polyhedron with ...