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Finite covers of a product of surfaces with bounded rank and arbitrarily large systole

  • Koji Fujiwara
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Abstract

We construct finite covers of a fixed product of two closed hyperbolic surfaces of genus two whose fundamental groups are generated by at most fifteen elements and whose injectivity radii tend to infinity. The construction uses fibre products over finite groups. These covers are closed aspherical four-manifolds with universal cover ℍ2×ℍ2. They give counterexamples to a conjecture of Avramidi and Delzant for symmetric spaces of higher rank, in the case ℍ2×ℍ2.

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Cite

BibTeXRIS
BibTeX
@misc{fujiwara2026finite,
  title = {{Finite covers of a product of surfaces with bounded rank and arbitrarily large systole}},
  author = {Koji Fujiwara},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21952},
  eprint = {2609.21952},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21952},
}
RIS
TY  - UNPB
TI  - Finite covers of a product of surfaces with bounded rank and arbitrarily large systole
AU  - Koji Fujiwara
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21952
UR  - https://arxiv.org/abs/2609.21952
AB  - We construct finite covers of a fixed product of two closed hyperbolic surfaces of genus two whose fundamental groups are generated by at most fifteen elements and whose injectivity radii tend to infinity. The construction uses fibre products over finite groups. These covers are closed aspherical four-manifolds with universal cover ℍ^2×ℍ^2. They give counterexamples to a conjecture of Avramidi and Delzant for symmetric spaces of higher rank, in the case ℍ^2×ℍ^2.
ER  -