Extensions of Sperner and Tucker's lemma for manifolds

Oleg R. Musin

Published 2012-12-09, updated 2014-03-26Version 2

The Sperner and Tucker lemmas are combinatorial analogous of the Brouwer and Borsuk - Ulam theorems with many useful applications. These classic lemmas are concerning labellings of triangulated discs and spheres. In this paper we show that discs and spheres can be substituted by large classes of manifolds with or without boundary.