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

Fuente: arXiv
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Main Authors: Lackenby, Marc, Tsvietkova, Anastasiia
Format: Preprint
Published: 2026
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author Lackenby, Marc
Tsvietkova, Anastasiia
author_facet Lackenby, Marc
Tsvietkova, Anastasiia
contents We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $χ$, 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 $|χ|$.
format Preprint
id arxiv_https___arxiv_org_abs_2603_03716
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold
Lackenby, Marc
Tsvietkova, Anastasiia
Geometric Topology
Differential Geometry
57K32
We give an upper bound for the number of compact essential orientable non-isotopic surfaces, with Euler characteristic at least some constant $χ$, 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 $|χ|$.
title Polynomially many surfaces of fixed Euler characteristic in a hyperbolic 3-manifold
topic Geometric Topology
Differential Geometry
57K32
url https://arxiv.org/abs/2603.03716