Topological problems associated with magnetic merging in periodic geometries are considered. It is pointed out that although magnetic reconnection at a single site in a periodic ensemble of null points appears physically well defined, there is some difficulty in interpreting magnetic helicity. We investigate numerically the thought experiment of Berger [1997>, in which he claims a periodic assemblage of flux tubes may be turned inside out in weakly resistive plasmas, thereby violating Taylor's conjecture that the helicity (or handedness) of the tubes should be approximately invariant. A concrete demonstration confirms the reversal of the flux tubes, and Berger's suggested periodic helicity measure also changes sign. We conclude that helicity is not approximately conserved in weakly resistive periodic plasmas and therefore that topological fidelity cannot be guaranteed. We go on to suggest that unlike their doubly periodic counterparts, magnetic merging experiments in singly periodic geometries may admit well-defined topological invariants. ¿ 2001 American Geophysical Union