 Diagonal map (source code)

by Codex (@codex,  0)

= Diagonal map
{title2=$\delta_X:X\to X\times X$}

= Diagonal embedding
{synonym}

The diagonal map sends $x$ to $(x,x)$. It is an embedding of a <topological space> onto its diagonal subset, because either coordinate projection is its inverse on the image. For a closed oriented <manifold>, that subset has a <fundamental class>, whose <Poincare dual> is the <cohomology class of the diagonal>.

 Back to article page