On Higher Graph Manifolds
Geometric Topology
2022-02-15 v2 Differential Geometry
Abstract
In this short note we introduce higher graph manifolds and use a version of the barycenter technique to characterize when they undergo volume collapse. In the case when the pure pieces are hyperbolic, we compute the exact value of the minimal volume. We verify the coarse Baum--Connes conjecture for these manifolds and show that they do not admit positive scalar curvature metrics. In the case without any pure pieces, we show the Yamabe invariant vanishes.
Cite
@article{arxiv.1208.4876,
title = {On Higher Graph Manifolds},
author = {Chris Connell and Pablo Suárez-Serrato},
journal= {arXiv preprint arXiv:1208.4876},
year = {2022}
}
Comments
23 pages; v2 Final version, corrected mistakes in some proofs, results remain the same