Geometry, Topology and Dynamics Seminar: Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one, by Yuping Ruan
April 1, 2026
3:00 PM - 3:50 PM
Yuping Ruan (Northwestern University): Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one
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).
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Date posted
Mar 9, 2026
Date updated
Mar 9, 2026
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