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The resistance of layered conductors with a multisheet Fermi surface (FS), ina high magnetic field, in the immediate vicinity of Lifshic's topologicaltransition when the separate FS sheets are drown together by an externalaction, pressure in part (and eventual change of the FS connectivity) isstudied theoretically. Analysis of magnetoresistance near topologicaltransition is illustrated for the case of FS in the shape of lightly corrugatedcylinder and two corrugated planes distributed with a repeated period in thepulse space. It yields, that as the FS plane sheets approach sufficiently thecylinder, the charge carriers produce a magnetic breakdown of one FS sheet toanother, decreasing a sharp anisotropy of magnetoresistance to the in-planecurrent. Instead of square increase with a magnetic field, the slowerresistance growth remains linear in the field within a broad magnetic-fieldrange. In the intimate vicinity of topological transition, when the energy gapbetween FS layers is negligibly small, the resistance is saturated.

Magnetoresistance of layered conductors under conditions of topological phase transition