Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold

Marc Lackenby; Anastasiia Tsvietkova

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arXiv · 2603.03716

Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold

Marc Lackenby·Anastasiia Tsvietkova

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Abstract

We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $\chi$, properly embedded in a finite-volume hyperbolic 3-manifold $M$, closed or cusped. This bound is a polynomial function of the volume of $M$, with degree that depends linearly on $|\chi|$.

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Marc Lackenby, Anastasiia Tsvietkova. 2026-03-04. Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold. https://arxiv.org/abs/2603.03716

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