In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space M sigma with singular stratum beta M (a closed manifold of positive codimension) and associated link equal to L, a smooth compact manifold. We briefly call such spaces manifolds with L-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 L is a simply connected homogeneous space of positive scalar curvature, L = G/H, with the semisimple compact Lie group G acting transitively on L by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed sufficient for large classes of examples, even when M sigma and beta M are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes.

Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants / Botvinnik, B; Piazza, P; Rosenberg, J. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 17:(2021). [10.3842/SIGMA.2021.062]

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

Piazza, P;
2021

Abstract

In this paper we continue the study of positive scalar curvature (psc) metrics on a depth-1 Thom-Mather stratified space M sigma with singular stratum beta M (a closed manifold of positive codimension) and associated link equal to L, a smooth compact manifold. We briefly call such spaces manifolds with L-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 L is a simply connected homogeneous space of positive scalar curvature, L = G/H, with the semisimple compact Lie group G acting transitively on L by isometries, we investigate when these necessary conditions are also sufficient. Our main result is that our conditions are indeed sufficient for large classes of examples, even when M sigma and beta M are not simply connected. We also investigate the space of such psc metrics and show that it often splits into many cobordism classes.
2021
positive scalar curvature; pseudomanifold; singularity; bordism; transfer; K-index; rho-invariant
01 Pubblicazione su rivista::01a Articolo in rivista
Positive Scalar Curvature on Spin Pseudomanifolds: the Fundamental Group and Secondary Invariants / Botvinnik, B; Piazza, P; Rosenberg, J. - In: SYMMETRY, INTEGRABILITY AND GEOMETRY: METHODS AND APPLICATIONS. - ISSN 1815-0659. - 17:(2021). [10.3842/SIGMA.2021.062]
File allegati a questo prodotto
File Dimensione Formato  
Botvinnik_Positive-scalar_2021.pdf

accesso aperto

Tipologia: Documento in Post-print (versione successiva alla peer review e accettata per la pubblicazione)
Licenza: Tutti i diritti riservati (All rights reserved)
Dimensione 544.43 kB
Formato Adobe PDF
544.43 kB Adobe PDF

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1677901
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 1
  • ???jsp.display-item.citation.isi??? 0
social impact