English

The signature of cusped hyperbolic 4-manifolds

Geometric Topology 2023-05-16 v4

Abstract

In this note we show that every integer is the signature of a non-compact, oriented, hyperbolic 4-manifold of finite volume, and give some partial results on the geography of such manifolds. The main ingredients are a theorem of Long and Reid, and the explicit construction of a hyperbolic 24-cell manifold with some special topological properties.

Keywords

Cite

@article{arxiv.2006.12095,
  title  = {The signature of cusped hyperbolic 4-manifolds},
  author = {Alexander Kolpakov and Stefano Riolo and Steven T. Tschantz},
  journal= {arXiv preprint arXiv:2006.12095},
  year   = {2023}
}

Comments

13 pages, 4 figures, 7 tables To appear in Int. Math. Res. Notices (minor changes wrt the previous version)