Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2021
• Main Authors: Botvinnik, Boris, Piazza, Paolo, Rosenberg, Jonathan
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2021
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211361
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants. Boris Botvinnik, Paolo Piazza and Jonathan Rosenberg. SIGMA 17 (2021), 062, 39 pages

In this paper, we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space Σ with singular stratum (a closed manifold of positive codimension) and associated link equal to , a smooth compact manifold. We briefly call such spaces manifolds with -fibered singularities. Under suitable spin assumptions, we give necessary index-theoretic conditions for the existence of wedge metrics of positive scalar curvature. Assuming in addition that is a simply connected homogeneous space of positive scalar curvature, = /, with the semisimple compact Lie group acting transitively on by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed enough for large classes of examples, even when Σ and are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes.