Topology Seminar - Yuping Ruan

Ohio State Garden of Constants
April 15, 2025
1:50 pm - 2:50 pm
Math Tower (MW) 152

Date Range
2025-04-15 13:50:00 2025-04-15 14:50:00 Topology Seminar - Yuping Ruan Yuping RuanNorthwestern UniversityTitleSimplicial volume and isolated, closed totally geodesic submanifolds of codimension oneAbstractWe 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 nontrivial Euclidean de Rham factors, or it has positive simplicial volume. This is based on a joint work with Chris Connell and Shi Wang, arXiv:2410.19981.For More Information About the Seminar Math Tower (MW) 152 America/New_York public

Yuping Ruan
Northwestern University

Title
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 nontrivial Euclidean de Rham factors, or it has positive simplicial volume. This is based on a joint work with Chris Connell and Shi Wang, arXiv:2410.19981.

For More Information About the Seminar

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