April 15, 2025
1:50 pm
-
2:50 pm
Math Tower (MW) 152
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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
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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.
