Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one
Geometric Topology
2024-10-29 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.2410.19981,
title = {Simplicial volume and isolated, closed totally geodesic submanifolds of codimension one},
author = {Chris Connell and Yuping Ruan and Shi Wang},
journal= {arXiv preprint arXiv:2410.19981},
year = {2024}
}
Comments
166 pages, 50 figures. Comments welcome!