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It is shown that the investigation of the conductivity in a single crystal of a normal metal with a complicated Fermi surface in strong magnetic fields B can reveal integral topological characteristics which are determined by the topology of open-ended quasiclassical electron trajectories. Specifically, in the case of open-ended trajectories of the general position there always exists a direction η orthogonal to B in which the conductivity approaches zero for large B, and this direction lies in some integral (i.e., generated by two reciprocal-lattice vectors) plane that remains stationary for small variations of the direction of B.

Topological quantum characteristics observed in the investigation of the conductivity in normal metals