Strong singularity for subalgebras of finite factors

In this paper we develop the theory of strongly singular subalgebras of von Neumann algebras, begun in earlier work. We mainly examine the situation of type $\tto$ factors arising from countable discrete groups. We give simple criteria for strong singularity, and use them to construct strongly singular subalgebras. We particularly focus on groups which act on geometric objects, where the underlying geometry leads to strong singularity.