Fitting for fluid-pressure pipelines

Cutting (1) for connecting a pressure-medium conduit (12), in particular according to DIN 2353 and ISO 8434-1, comprising a connection piece (4), one with the connecting piece (4) screw-nut (6) and a between the connecting piece (4) and the union nut (6) arranged, metallic cutting ring (20) for cutting having at least one cutting edge (30) into the pipeline (12), wherein the cutting ring (20) at least a substantial contemporary sealing surface (40, 44) for the direct, metallic sealing contact against a mating sealing surface (42, 46), characterized in that in the region of the sealing surface (40; 44) has a grooving of a plurality of circumferential, groove-like, such a fine groove (54) is formed such that in the mounted, against the counter-sealing surface (42; 46) compressed state fine capillary annular chambers (56) are formed.