Two geometries touch if the intersection of their interiors is empty, but the intersection of the two geometries is not empty.

Example 1: Does Geometry A touch Geometry B?

static boolean geometryTouches(Geometry geometryA, Geometry geometryB, SpatialReference sr)
{
  boolean touches = OperatorTouches.local().execute(geometryA, geometryB, sr, null);
  return touches;
}