Work

On Higher Graph Manifolds

Year: 2017

Type: article

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.

Source: International Mathematics Research Notices

DOI: 10.1093/imrn/rnx133

Authors: C Connell, P Suàrez-Serrato

Institutions: Indiana University Bloomington, Indiana University, Universidad Nacional Autónoma de México

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Simons Foundation, Consejo Nacional de Ciencia y Tecnología, Centre National de la Recherche Scientifique, Universidad Nacional Autónoma de México

Award: G1819458354