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 ; Versió publicada
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

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/295189
DOI: 10.5565/PUBLMAT_59215_04

13 p, 395.6 KB

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