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H 1 ALC manifolds with exceptional holonomy

Auteurs : Foscolo, Lorenzo (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : We will describe the construction of complete non-compact Ricci-flat manifolds of dimension 7 and 8 with holonomy $G_{2}$ and Spin(7) respectively. The examples we consider all have non-maximal volume growth and an asymptotic geometry, so-called ALC geometry, that generalises to higher dimension the asymptotic geometry of 4-dimensional ALF hyperkähler metrics. The interest in these metrics is motivated by the study of codimension 1 collapse of compact manifolds with exceptional holonomy. The constructions we will describe are based on the study of adiabatic limits of ALC metrics on principal Seifert circle fibrations over asymptotically conical orbifolds, cohomogeneity one techniques and the desingularisation of ALC spaces with isolated conical singularities. The talk is partially based on joint work with Mark Haskins and Johannes Nordstrm.

    Keywords : $G_{2}$ manifold; Einstein metric; spin (7) manifold

    Codes MSC :
    53C10 - $G$-structures
    53C25 - Special Riemannian manifolds (Einstein, Sasakian, etc.)
    53C29 - Issues of holonomy [
    53C80 - Applications of global differential geometry to physics

    Informations sur la rencontre

    Nom de la rencontre : Méthodes microlocales en analyse et géométrie / Microlocal Methods in Analysis and Geometry
    Organisateurs de la rencontre : Carron, Gilles ; Mazzeo, Rafe ; Piazza, Paolo ; Wunsch, Jared
    Dates : 06/05/2019 - 10/05/2019
    Année de la rencontre : 2019
    URL Congrès : https://conferences.cirm-math.fr/1988.html

    Citation Data

    DOI : 10.24350/CIRM.V.19521203
    Cite this video as: Foscolo, Lorenzo (2019). ALC manifolds with exceptional holonomy. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19521203
    URI : http://dx.doi.org/10.24350/CIRM.V.19521203

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