Epimorphism sequences between hyperbolic 3-manifold groups

Constructing Non-congruence Subgroups of Flexible Hyperbolic 3-manifold Groups

We give an explicit construction for non-congruence subgroups in the fundamental group of a flexible hyperbolic 3-manifold.

Which 3-manifold Groups Are Kähler Groups?

The question in the title, first raised by Goldman and Donaldson, was partially answered by Reznikov. We give a complete answer, as follows: if G is both a (closed) 3-manifold group and a Kähler group, then G must be finite.

Isospectrality and 3-manifold Groups

In this note, we explain how a well-known construction of isospectral manifolds leads to an obstruction to a group being the fundamental group of a closed 3-dimensional manifold. The problem of determining, for a given group G, whether there is a closed 3-manifold M with π1(M) ∼= G is readily seen to be undecidable; let us write G ∈ G 3 if there is such a 3-manifold. A standard conjecture (rela...

Non-manifold Hyperbolic Groups of High Cohomological Dimension

COMPLEX HYPERBOLIC (3, 3, n) TRIANGLE GROUPS

Complex hyperbolic triangle groups are representations of a hyperbolic (p, q, r) reflection triangle group to the group of holomorphic isometries of complex hyperbolic space H C , where the generators fix complex lines. In this paper, we obtain all the discrete and faithful complex hyperbolic (3, 3, n) triangle groups. Our result solves a conjecture of Schwartz [16] in the case when p = q = 3.