  We solve the problem of determining basic topological properties of flat
samples by performing measurements on their outer edge. The global maximum of
four probe resistances shows a characteristic behaviour, which is dependent on
the genus (i.e., the number of holes) of the domain. An extension of the van
der Pauw method on domains having zero, one, or two holes is presented and
discussed. A possibility of measuring topological properties of condensed
matter is demonstrated. Experimental results for triply connected domains are
presented and explained by continuous symmetry breaking caused by the presence
of two holes. The results are consistent with the topological theorem of
Hurwitz on the number of automorphisms of Riemann surfaces.
