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The portion of a surface left when an open disk is removed from it.

The knot move obtained by fixing disk 1 in the figure above and flipping disks 2 and 3.

For a system of n first-order ordinary differential equations (or more generally, Pfaffian forms), the 2n-dimensional space consisting of the possible values of ...

Let (xi_1,xi_2) be a locally Euclidean coordinate system. Then ds^2=dxi_1^2+dxi_2^2. (1) Now plug in dxi_1=(partialxi_1)/(partialx_1)dx_1+(partialxi_1)/(partialx_2)dx_2 (2) ...

The plumbing of a p-sphere and a q-sphere is defined as the disjoint union of S^p×D^q and D^p×S^q with their common D^p×D^q, identified via the identity homeomorphism. This ...

The index of a vector field with finitely many zeros on a compact, oriented manifold is the same as the Euler characteristic of the manifold.

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.

The Reidemeister move of type II.

The homeomorphic image of a so-called "complete separable" metric space. The continuous image of a Polish space is called a Souslin set.

A knot equivalent to a polygon in R^3, also called a tame knot. For a polygonal knot K, there exists a plane such that the orthogonal projection pi on it satisfies the ...