Real Bott manifolds and acyclic digraphs

TL;DR

This paper offers a combinatorial approach to classifying real Bott manifolds using operations on directed acyclic graphs, leading to new invariants and a deeper understanding of their structure.

Contribution

It introduces a novel combinatorial characterization of real Bott manifolds via acyclic digraph operations, expanding on Masuda's matrix-based description.

Findings

New invariants for real Bott manifolds

Graph-based characterization of diffeomorphism classes

Enhanced understanding of manifold structure

Abstract

Masuda (2008) provided the characterization of real Bott manifolds in terms of three operations on upper triangular matrices. We provide a combinatorial characterization of real Bott manifolds up to diffeomorphism in terms of operations on directed acyclic graphs. Our observation leads to several new invariants of real Bott manifolds.