Dodecahedral L-spaces and hyperbolic 4-manifolds
Geometric Topology
2024-12-23 v2
Abstract
We prove that exactly 6 out of the 29 rational homology 3-spheres tessellated by four or less right-angled hyperbolic dodecahedra are L-spaces. The algorithm used is based on the L-space census provided by Dunfield in arXiv:1904.04628, and relies on a result by Rasmussen-Rasmussen arXiv:1508.05900. We use the existence of these manifolds together with a result of Martelli arXiv:1510.06325 to construct explicit examples of hyperbolic 4-manifolds containing separating L-spaces, and therefore having vanishing Seiberg-Witten invariants. This answers a question asked by Agol and Lin in arXiv:1812.06536.
Cite
@article{arxiv.2208.01542,
title = {Dodecahedral L-spaces and hyperbolic 4-manifolds},
author = {Ludovico Battista and Leonardo Ferrari and Diego Santoro},
journal= {arXiv preprint arXiv:2208.01542},
year = {2024}
}
Comments
39 pages, 10 figures, 6 tables. Accepted for publication in Communications in Analysis and Geometry