Symmetry, Integrability and Geometry: Methods and Applications
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


SIGMA:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Symmetry, Integrability and Geometry: Methods and Applications, 2024, Volume 20, 069, 22 pp.
DOI: https://doi.org/10.3842/SIGMA.2024.069 (Mi sigma2071) 		 
Torsion Obstructions to Positive Scalar Curvature

Misha Gromovab, Bernhard Hankec

a Courant Institute of Mathematical Sciences, New York University, New York, NY 10012-1185, USA
b Institut des Hautes Études Scientifiques, 91893 Bures-sur-Yvette, France
c Institut für Mathematik, University of Augsburg, 86135 Augsburg, Germany
Full-text PDF (556 kB)
References:
PDF
HTML
DOI: https://doi.org/10.3842/SIGMA.2024.069
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: positive scalar curvature, toral manifold, enlargeability, $\mu$-bubble; group homology, Riemannian foliation, band width inequality.
Funding agency Grant number
Deutsche Forschungsgemeinschaft
B.H. acknowledges support from NYU, the IAS Princeton and the DFG-funded Special Priority Program 2026 Geometry at Infinity.
Received: November 7, 2023; in final form July 17, 2024; Published online July 30, 2024
Document Type: Article
MSC: 53C21, 53C23, 20J06, 53C12, 55N10
Language: English
Citation: Misha Gromov, Bernhard Hanke, “Torsion Obstructions to Positive Scalar Curvature”, SIGMA, 20 (2024), 069, 22 pp.
Citation in format AMSBIB
\Bibitem{GroHan24}
\by Misha~Gromov, Bernhard~Hanke
\paper Torsion Obstructions to Positive Scalar Curvature
\jour SIGMA
\yr 2024
\vol 20
\papernumber 069
\totalpages 22
\mathnet{http://mi.mathnet.ru/sigma2071}
\crossref{https://doi.org/10.3842/SIGMA.2024.069}
Linking options:
  • https://www.mathnet.ru/eng/sigma2071
  • https://www.mathnet.ru/eng/sigma/v20/p69
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Symmetry, Integrability and Geometry: Methods and Applications
    Statistics & downloads:
    Abstract page:20
    Full-text PDF :10
    References:10
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024