On the topology of singularities of the set of supporting hyperplanes of a smooth submanifold in an affine space

• Autores: V. D. Sedykh
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 71, Nº 1, 2005, págs. 259-272
• Idioma: inglés
• DOI: 10.1112/s0024610704006003
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• Resumen

  • Many new universal relations are obtained between the Euler numbers of manifolds of singular supporting hyperplanes of an arbitrary generic smooth closed -dimensional submanifold in where or . These relations are applied to Barner-convex curves in an odd-dimensional space . A universal (nontrivial) linear relation is established between the numbers of singular supporting hyperplanes of various types but of the same total multiplicity of tangency with a given generic smooth closed connected Barner-convex curve in . The coefficients of this relation are defined by Catalan numbers.