Magnetic connectivity of coronal fields: geometrical versus topological description

We analyse the mapping produced by the field lines which connect photospheric areas of positive and negative magnetic polarity on the Sun. The geometrical quantities independent of the direction of such a mapping (from positive to negative polarity, and vice versa) are introduced. They yield a complete description of the field line connectivity in coronal magnetic configurations and, in particular, in quasi-separatrix layers (QSLs). The elementary magnetic flux tubes are enormously squashed in QSLs without giving the true jump in the field-line mapping, as it occurs at the genuine separatrix surfaces. So the QSLs may be present even in topologically trivial magnetic configurations. This is illustrated by an example relevant to solar flare events.