Torsion Obstructions to Positive Scalar Curvature

Misha Gromov; Bernhard Hanke

doi:10.3842/SIGMA.2024.069

Torsion Obstructions to Positive Scalar Curvature

Misha Gromov, Bernhard Hanke

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.

Original language	English (US)
Article number	069
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	20
DOIs	https://doi.org/10.3842/SIGMA.2024.069
State	Published - 2024

Keywords

band width inequality
enlargeability
group homology
positive scalar curvature
Riemannian foliation
toral manifold
µ-bubble

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

Access to Document

10.3842/SIGMA.2024.069

Cite this

@article{f93f0b9279734b1ba180ebca1dcb5577,

title = "Torsion Obstructions to Positive Scalar Curvature",

abstract = "We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.",

keywords = "band width inequality, enlargeability, group homology, positive scalar curvature, Riemannian foliation, toral manifold, µ-bubble",

author = "Misha Gromov and Bernhard Hanke",

year = "2024",

doi = "10.3842/SIGMA.2024.069",

language = "English (US)",

volume = "20",

journal = "Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)",

issn = "1815-0659",

publisher = "Department of Applied Research, Institute of Mathematics of National Academy of Science of Ukraine",

}

TY - JOUR

T1 - Torsion Obstructions to Positive Scalar Curvature

AU - Gromov, Misha

AU - Hanke, Bernhard

PY - 2024

Y1 - 2024

N2 - We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.

AB - We study obstructions to the existence of Riemannian metrics of positive scalar curvature on closed smooth manifolds arising from torsion classes in the integral homology of their fundamental groups. As an application, we construct new examples of manifolds which do not admit positive scalar curvature metrics, but whose Cartesian products admit such metrics.

KW - band width inequality

KW - enlargeability

KW - group homology

KW - positive scalar curvature

KW - Riemannian foliation

KW - toral manifold

KW - µ-bubble

UR - http://www.scopus.com/inward/record.url?scp=85201591288&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85201591288&partnerID=8YFLogxK

U2 - 10.3842/SIGMA.2024.069

DO - 10.3842/SIGMA.2024.069

M3 - Article

AN - SCOPUS:85201591288

SN - 1815-0659

VL - 20

JO - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

JF - Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

M1 - 069

ER -

Torsion Obstructions to Positive Scalar Curvature

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this