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Tout chemin générique de hérissons réalisant un retournement de la sphère dans R3 comprend un hérisson porteur de queues d’aronde positives
Martinez-Maure, Yves (Institut Mathématique de Jussieu (París, França))

Data: 2015
Resum: Hedgehogs are (possibly singular and self-intersecting) hypersurfaces that describe Minkowski differences of convex bodies in Rn+1. They are the natural geometrical objects when one seeks to extend parts of the Brunn–Minkowski theory to a vector space which contains convex bodies. In this paper, we prove that in every generic path of hedgehogs performing the eversion of the sphere in R3, there exists a hedgehog that has positive swallowtails. This study was motivated by an open problem raised in 1985 by Langevin, Levitt, and Rosenberg.
Drets: Tots els drets reservats
Llengua: Francès.
Document: article ; recerca ; publishedVersion
Matèria: Eversion of the sphere ; Hedgehogs ; Generic metamorphosis ; Type of swallowtails ; Indices ; Absolute coorientation
Publicat a: Publicacions matemàtiques, Vol. 59 Núm. 2 (2015) , p. 339-351 (Articles) , ISSN 2014-4350

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DOI: 10.5565/PUBLMAT_59215_04

13 p, 395.6 KB

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