Colorings of simplicial complexes and vector bundles over Davis-Januszkiewicz spaces

TL;DR

This paper explores how coloring properties of simplicial complexes relate to the splitting characteristics of associated vector bundles over Davis-Januszkiewicz spaces, linking combinatorics with algebraic topology.

Contribution

It establishes a connection between coloring properties of simplicial complexes and the splitting of vector bundles via Chern classes on Davis-Januszkiewicz spaces, a novel interdisciplinary approach.

Findings

Coloring properties are reflected in bundle splitting behavior.

Chern classes are expressed through elementary symmetric polynomials.

Provides a new perspective linking combinatorics and topology.

Abstract

We show that coloring properties of a simplicial complex K are reflected by splitting properties of a bundle over the associated Davis-Januszkiewicz space whose Chern classes are given by the elementary symmetric polynomials in the generators of the Stanley-Reisner algebra of K.