Uniform spectral gap of scl in $2$-orbifolds

Lvzhou Chen; Nicolaus Heuer

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arXiv · 2604.21059

Uniform spectral gap of scl in $2$-orbifolds

Lvzhou Chen·Nicolaus Heuer

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Abstract

We show a uniform spectral gap of stable commutator length for all compact hyperbolic $2$-orbifolds relative to the peripheral subgroups. Except for the case of a sphere with three cone points, we have an explicit uniform gap $1/36$. These estimates are needed in understanding stable commutator length in $3$-manifolds. Our methods use explicit quasimorphisms for the generic case, and use hyperbolic geometry (pleated surfaces) for the exceptional case of a sphere with three cone points.

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Lvzhou Chen, Nicolaus Heuer. 2026-04-22. Uniform spectral gap of scl in $2$-orbifolds. https://arxiv.org/abs/2604.21059

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