Non-abelian expansion in octonionic hyperbolic manifolds.

  • Tagungsort:

    Geb. 20.30, SR 1.067

  • Datum:

    19.11.2024

  • Referent:

    Mikolaj Fraczyk

  • Zeit:

    14:00 Uhr

  • Abstract: Let M be a compact octonionic hyperbolic manifold. Assuming only lower bound on the systole of M, we show that any branched cover of M with branching locus of small volume can be efficiently cut and reconnected to create a genuine cover. It is a Riemannian analogue of the cover stability phenomenon described by Dinur and Meshulam, which can be rephrased using isoperimetric inequalities for cocycles valued in symmetric groups. For the proof we think of the branching locus as a codimension 2 soap bubble which deforms to minimize its volume. We show that if such bubble isn’t big enough then it always collapses to a codimension 3-subset. This relates the original problem to the study of minimal submaniflds of octonionic hyperbolic manifolds. Based on a joint work with Ben Lowe.