On the theorems of Borsuk-Ulman and Ljusternik-Shnirelman-Borsuk

Abstract

The main result: Every homotopically trivial map $f:X\to M^n$ from the $(n-1)$-connected space $X$ with involution $\phi$ to the $n$-dimensional topological manifold $M^n$ identifies a pair of points $(x,\phi (x))$