APPLICATION OF TOPOLOGICAL METHODS TO ESTIMATE THE NUMBER OF LONGITUDINAL ELASTIC-WAVES IN CRYSTALS

In the problem of estimating the number of longitudinal normals of ela stic waves in crystals, several approaches based on the methods of mod ern topology and associated with the use of topological invariants are proposed. It is shown that for any symmetry class of the crystals the re exists not less than three directions along which purely longitudin al waves can propagate. Under the Morse condition on the fundamental f unction, connections are obtained between the numbers of directions of longitudinal normals corresponding to different types of critical poi nts of this function. Further prospects are discussed.