On the topology of wave fronts in spaces of low dimension (Q2889561)
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scientific article; zbMATH DE number 6043637
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the topology of wave fronts in spaces of low dimension |
scientific article; zbMATH DE number 6043637 |
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On the topology of wave fronts in spaces of low dimension (English)
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8 June 2012
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wave fronts
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(multi)singularities
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adjacency index
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contact structure
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Legendrian manifold
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Legendrian singularity
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Legendrian stability
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Euler characteristic
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The author calculates the adjacency indices for all singularities of generic wave fronts in spaces of dimension \(n\leq 6\). These computations are used to find all linear relations with real coefficients between the Euler characteristics of manifolds of singularities of a compact generic wave front in any smooth \(n\)-dimensional manifold. Other results connected to this topic are contained in the author's papers [Funct. Anal. Appl. 37, No. 2, 123--133 (2003); translation from Funkts. Anal. Prilozh. 37, No. 2, 52--64 (2003; Zbl 1048.32020)] and [ibid. 38, No. 4, 298--301 (2004); translation from Funkts. Anal. Prilozh. 38, No. 4, 73--78 (2004; Zbl 1072.58027)].
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