Lower bounds on complexity of geometric 3-orbifolds

TL;DR

This paper establishes a lower bound on the complexity of orientable geometric 3-orbifolds using Delzant's T-invariants, extending known bounds from 3-manifolds to orbifolds.

Contribution

It generalizes existing complexity bounds from 3-manifolds to the broader class of geometric 3-orbifolds by relating them to orbifold-fundamental groups.

Findings

Lower bounds on orbifold complexity in terms of T-invariants

Extension of 3-manifold complexity bounds to orbifolds

Framework for analyzing orbifold complexity using algebraic invariants

Abstract

We establish a lower bound on the complexity orientable locally orientable geometric 3-orbifolds in terms of Delzant's T-invariants of their orbifold-fundamental groups, generalizing previously known bounds for complexity of 3-manifolds.