Spring 2026 Berstein Seminar

Some possible readings

Background

• Martelli, An Introduction to Geometric Topology

• Ratcliffe, Foundations of Hyperbolic Manifolds

Four-manifolds (lots more to be found in the references in the survey)

• Martelli, Hyperbolic four-manifolds, Handbook of group actions. Vol. III, 37–58.  (arXiv)

• Ivansic, Ratcliffe, Tschantz.  Complements of tori and Klein bottles in the 4-sphere that have hyperbolic structure. Algebr. Geom. Topol. 5 (2005), 999–1026.

Hyperbolic 5-manifolds fibering over the circle

• Italiano, Martelli, Migliorini.  Hyperbolic 4-manifolds that fiber over S^1.  Invent. Math. 231 (2023), 1-38.

• Martelli, A 4-dimensional pseudo-Anosov homeomorphism (arXiv:2511.10530)

Even higher dimensions

• Italiano, Martelli, Migliorini.  Hyperbolic manifolds that fiber algebraically up to dimension 8.  J. Inst. Math. Jussieu 23 (2024), 609-646.

Complex hyperbolic manifolds

• There's a brief introduction to the complex (and quaternionic) hyperbolic spaces in Chapter II.10 of Bridson&Haefliger.

• Thurston, Shapes of polyhedra and triangulations of the sphere.  Geometry & Topology Monographs 1 (1998) 511–549

• Kojima, Complex hyperbolic cone structures on the configuration spaces. Rend. Istit. Mat. Univ. Trieste

Suppl. 1 Vol. XXXII, 149–163 (2001)

• Llosa Isenrich, C., Py, P. Subgroups of hyperbolic groups, finiteness properties and complex hyperbolic lattices. Invent. math. 235, 233–254 (2024).