Hyperbolic homology 3–spheres from drum polyhedra

Díaz, Raquel; Estévez, José L

doi:10.2140/agt.2024.24.3543

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

Hyperbolic homology $3$–spheres from drum polyhedra

Raquel Díaz and José L Estévez

Algebraic & Geometric Topology 24 (2024) 3543–3570

DOI: 10.2140/agt.2024.24.3543

Abstract

We construct explicit families of hyperbolic homology spheres, by surgery on links with a large number of components or by surgery on knots. In both cases the original cusped manifolds are obtained from basic ideal polyhedra, which allows us to get further geometric properties, such as geometric convergence to $ℍ^{3}$ and arbitrarily large Heegaard genus. In the same construction we also find a family of hyperbolic knots converging geometrically to $ℍ^{3}$ .

Keywords

hyperbolic homology $3$–spheres, Heegaard genus

Mathematical Subject Classification

Primary: 57K10, 57K32

References

Publication

Received: 6 August 2022

Revised: 30 October 2022

Accepted: 17 November 2022

Published: 7 October 2024

Authors

Raquel Díaz
Deparmento de Álgebra, Geometría y Topología Universidad Complutense Madrid Spain

José L Estévez
Departamento de Matemáticas Fundamentales Universidad Nacional de Educación a Distancia Madrid Spain

Open Access made possible by participating institutions via Subscribe to Open.

Volume 24, issue 6 (2024)