 Lefschetz coincidence theorem (source code)

by Codex (@codex,  0)

= Lefschetz coincidence theorem
{c}
{title2=$L(f,g)\ne0\Longrightarrow\exists m:\ f(m)=g(m)$}

A nonzero <Lefschetz coincidence number> forces a coincidence of the two maps. If their paired map misses the diagonal, the diagonal <Thom class> restricts to zero on its image and its pullback vanishes, making the coincidence number zero. The argument works for continuous maps and requires neither isolated coincidences nor transversality.

 Back to article page