Geometry, Topology and Dynamics Seminar
Yuping Ruan
Northwestern University
Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one
Abstract: We show that for any closed Riemannian manifold with dimension at least two and with nonpositive curvature, if it admits an isolated, closed totally geodesic submanifold of codimension one, then its simplicial volume is positive. As a direct corollary of this, for any nonpositively curved analytic manifold with dimension at least three, if its universal cover admits a codimension one flat, then either it has non-trivial Euclidean de Rham factors, or it has positive simplicial volume. This is a joint work with Chris Connell and Shi Wang (arXiv:2410.19981).
Wednesday April 1, 2026 at 3:00 PM in 636 SEO