Uniform spectral gap of scl in $2$-orbifolds

Lvzhou Chen; Nicolaus Heuer

Uniform spectral gap of scl in $2$-orbifolds

Geometric Topology 2026-05-28 v2 Group Theory

Authors: Lvzhou Chen , Nicolaus Heuer

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.

Keywords

stable commutator length spectral gap hyperbolic orbifold quasimorphism pleated surface 3-manifold

Cite

@article{arxiv.2604.21059,
  title  = {Uniform spectral gap of scl in $2$-orbifolds},
  author = {Lvzhou Chen and Nicolaus Heuer},
  journal= {arXiv preprint arXiv:2604.21059},
  year   = {2026}
}

Comments

v2: minor revision, added acknowledgment; 20 pages, 4 figures. This is separated from the authors' earlier paper arXiv:1910.14146, which was shortened for publication purposes

Uniform spectral gap of scl in $2$-orbifolds

Abstract

Keywords

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