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JOURNALS // Moscow Mathematical Journal // Archive

Mosc. Math. J., 2011 Volume 11, Number 3, Pages 583–598 (Mi mmj434)

This article is cited in 3 papers

On the topology of cooriented wave fronts in spaces of small dimensions

V. D. Sedykh

Department of Higher Mathematics, Russian State University of Oil and Gas (Gubkin), Moscow, Russia

Abstract: We consider Legendre singularities with respect to Legendre equivalence preserving a coorientation of the contact structure. In this case, we calculate the adjacency indices of multisingularities of generic Legendre mappings to smooth manifolds of the dimension $n\leq6$. As a corollary, we find new coexistence conditions on singularities of wave fronts. Namely, we find all linear relations with real coefficients between the Euler characteristics of manifolds of singularities of any generic compact cooriented wave front in any $n$-dimensional space.

Key words and phrases: Legendre mappings, wave fronts, (multi)singularities, adjacency index, Euler characteristic.

MSC: 57R45, 58K30

Received: December 29, 2010

Language: English



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