Abstract:Let $M$ be a closed orientable $3$-manifold admitting a metric of nonpositive sectional curvature (an NPC metric), and let $G$ be a finite group acting freely on $M$ by orientation-preserving diffeomorphisms. Previous results showed that $M$ admits a $G$-invariant NPC metric except possibly when $M$ is a graph manifold. In this paper, we resolve the remaining case by proving that $M$ also admits a $G$-invariant NPC metric when $M$ is a graph manifold. This result advances our understanding in dimension $3$ of the question posed by Schoen-Yau about Nielsen realization for NPC $3$-manifolds.
From: Zhengyu Zou [view email]
[v1]
Sat, 20 Jun 2026 15:12:54 UTC (77 KB)
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