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Topology of the intersections of ellipsoids in \(\mathbf{R}^n\)

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Abstract

We present an overview of work, including unpublished results, on the characterization and description of the topological type of the differentiable manifolds that are diffeomorphic to a transverse intersection of ellipsoids in euclidean space, subject to certain conditions regarding the type and the number of them.

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Notes

  1. The equivalence of (a) and (b) in Theorems 1 and 2 was proved in 1972 in the unpublished 3ème Cycle thesis by Michel Herman [17]. The proofs are quite long and use deep results from the theory of real analytic functions and unpublished results by R.Palais. Unaware of this, we proved these theorems in 2004 [14], following the steps of the proof by Tognoli of the Nash conjecture (see [4]). After learning from Alain Chenciner the existence of [17] our proofs remained unpublished waiting for a revision of the preprint.

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Acknowledgements

The authors were partially supported by Project PAPIIT-IN111415, UNAM.

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Authors and Affiliations

  1. Facultad de Ciencias, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Vinicio Gómez-Gutiérrez

  2. Instituto de Matemáticas, Universidad Nacional Autónoma de México, Mexico City, Mexico

    Santiago López de Medrano

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  1. Vinicio Gómez-Gutiérrez
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  2. Santiago López de Medrano
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Correspondence to Santiago López de Medrano.

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This article is dedicated to Maite Lozano.

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Gómez-Gutiérrez, V., López de Medrano, S. Topology of the intersections of ellipsoids in \(\mathbf{R}^n\). RACSAM 112, 879–891 (2018). https://doi.org/10.1007/s13398-018-0552-6

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  • DOI: https://doi.org/10.1007/s13398-018-0552-6

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