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A metric characterizing the difference between two knots K and K^' in S^3.

A branch of mathematics which brings together ideas from algebraic geometry, linear algebra, and number theory. In general, there are two main types of K-theory: topological ...

The Betti numbers of a compact orientable n-manifold satisfy the relation b_i=b_(n-i).

A C^infty (infinitely differentiable) manifold is said to be a submanifold of a C^infty manifold M^' if M is a subset of M^' and the identity map of M into M^' is an ...

An ambient isotopy from an embedding of a manifold M in N to another is a homotopy of self diffeomorphisms (or isomorphisms, or piecewise-linear transformations, etc.) of N, ...

The approximation problem is a well known problem of functional analysis (Grothendieck 1955). It asks to determine whether every compact operator T from a Banach space X to a ...

All closed surfaces, despite their seemingly diverse forms, are topologically equivalent to spheres with some number of handles or cross-caps. The traditional proof follows ...

There are several different definition of link. In knot theory, a link is one or more disjointly embedded circles in three-space. More informally, a link is an assembly of ...

An oriented link is a link for which each connected component has been given an orientation. As oriented links are equivalent, if there is an orientation preserving ...

A technical conjecture which connects algebraic K-theory to étale cohomology. The conjecture was made more precise by Dwyer and Friedlander (1982). Thomason (1985) ...