arXiv subjects

Alan W. Reid

Publications and source records attributed to Alan W. Reid.

38 records · Page 3Linked to original sources

arXiv2001

The Bianchi groups are subgroup separable on geometrically finite subgroups

We show that for certain arithmetic groups, geometrically finite subgroups are the intersection of finite index subgroups containing them. Examples are the Bianchi groups and the Seifert-Weber dodecahedral space. In particular, for manifolds commensurable with these groups, immersed incompressible surfaces lift to embeddings in a finite sheeted covering.

math.GT↗

arXiv2000

Generalized Hopfian property, minimal Haken manifold, and J. Simon's conjecture for 3-manifold groups

We address a conjecture that $π_1$-surjective maps between closed aspherical 3-manifolds having the same rank on $π_1$ must be of non-zero degree. The conjecture is proved for Seifert manifolds, which is used in constructing the first known example of minimum Haken manifold. Another motivation is to study epimorphisms of 3-manifold groups via maps of non-zero degree between 3-manifolds.

math.GT↗