Subgroup Separability and Incompressible Immersions
by
Saburo Matsumoto
Tokyo Institute of Technology
Coauthors: Iain R. Aitchison, J. Hyam Rubinstein

The main theme of this talk is the ''separability of surfaces'' in 3-manifolds. Given an incompressible surface F immersed in a 3-manifold M, when can F be lifted to an embedding in some finite cover of M? This question is related to such concepts as virtually Haken 3-manifolds, virtual Z-representability of \pi₁(M), the rigidity of M, and the subgroup separability of \pi₁(M). If \pi₁(M) is subgroup separable (or LERF), every incompressible immersion lifts to an embedding in a finite cover of M. These surfaces are called ``virtually embedded'' or ``separable.''

I will state some known results about separable and non-separable surfaces and give examples of these. In particular, I will mention some properties of \pi₁(M) when M admits a ``cubing, '' such as its automatic structure.

Date received: April 24, 1998