Rainbow simplices in triangulations of manifolds

TL;DR

This paper investigates conditions under which a colored triangulation of a manifold guarantees the existence of a simplex with all vertices differently colored, using homological methods to analyze the problem.

Contribution

It introduces homological criteria for rainbow simplices in colored triangulations of manifolds, advancing understanding of combinatorial topology.

Findings

Homological conditions ensure rainbow simplices in certain triangulations.

Provides new criteria linking coloring and topological properties.

Extends previous results to broader classes of manifolds.

Abstract

Given a coloration of the vertices of a triangulation of a manifold, we give homological conditions on the chromatic complexes under which it is possible to obtain a rainbow simplex