Work

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

Year: 2026

Type: preprint

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 $\mathbb H^2\times\mathbb H^2$. They give counterexamples to a conjecture of Avramidi and Delzant for symmetric spaces of higher rank, in the case $\mathbb H^2\times\mathbb H^2$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2609.21952

Author: Fujiwara, Koji

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: University of Oxford, Japan Society for the Promotion of Science, Mathematical Institute, University of Oxford

Award: 離散群に潜む新しい構造の発見と解明

OpenAlex ID: W7213912190

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