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

Abstract

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