Corpus ID: 119155233

# Systolic volume and complexity of 3-manifolds

@article{Chen2015SystolicVA,
title={Systolic volume and complexity of 3-manifolds},
author={Lizhi Chen},
journal={arXiv: Geometric Topology},
year={2015}
}
• Lizhi Chen
• Published 2015
• Mathematics
• arXiv: Geometric Topology
• Let $M$ be an orientable closed irreducible $3$-manifold. We prove that if $M$ is aspherical, the systolic volume of $M$, denoted $\text{SR}(M)$, is bounded below in terms of the complexity. This result shows that the systolic volume of $3$-manifolds has the finiteness property. For any positive real number $T$, there are only a finite number of closed irreducible aspherical $3$-manifolds $M$ with $\text{SR}(M) < T$.