Suppose $\Gamma$ is a lattice in $PSL(2, \mathbb{R})$ acting on the upper half plane. Suppose that the stabilizer in $\Gamma$ of the point at infinity is nontrivial. Does it then follow that the exists a Dirichlet domain for $\Gamma$ which has a vertex at infinity?
2026-04-01 09:31:54.1775035914
Does a lattice in $PSL(2,\mathbb{R})$ stabilizing $\infty$ have a domain with vertex at $\infty$?
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