Corpus ID: 119155233

Systolic volume and complexity of 3-manifolds

  title={Systolic volume and complexity of 3-manifolds},
  author={Lizhi Chen},
  journal={arXiv: Geometric Topology},
  • 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 $\text{SR}(M) < T$. 


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