A note on large torsion in $\mathbb{Q}$-acyclic complexes

TL;DR

This paper introduces new upper bounds on the torsion group size of $Q$-acyclic simplicial complexes, based solely on their vertex degree sequence and dimension, advancing understanding of their algebraic topology.

Contribution

It provides novel upper bounds for torsion groups in $Q$-acyclic complexes that depend only on vertex degrees and dimension, offering a new approach to their analysis.

Findings

Derived explicit upper bounds for torsion groups

Bounds depend only on vertex degree sequence and dimension

Enhances understanding of algebraic properties of $Q$-acyclic complexes

Abstract

New upper bounds on the size of the torsion group of a $\mathbb{Q}$-acyclic simplicial complex are introduced which depend only on the vertex degree sequence of the complex and its dimension.