On Higher Graph Manifolds. (17th July 2017)

• Record Type: Journal Article
• Authors: Connell, C; Suàrez-Serrato, P
• Is Part Of: International mathematics research notices. Volume 2019:Number 5(2019)
• Page Start: 1281
• Page End: 1311
• Publication Date: 2017-07-17
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnx133
• Languages: English
• ISSNs: 1073-7928

Abstract

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.