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- Title
Positive scalar curvature on simply connected spin pseudomanifolds.
- Authors
Botvinnik, Boris; Piazza, Paolo; Rosenberg, Jonathan
- Abstract
Let M Σ be an n -dimensional Thom–Mather stratified space of depth 1. We denote by β M the singular locus and by L the associated link. In this paper, we study the problem of when such a space can be endowed with a wedge metric of positive scalar curvature. We relate this problem to recent work on index theory on stratified spaces, giving first an obstruction to the existence of such a metric in terms of a wedge α -class α w (M Σ) ∈ KO n . In order to establish a sufficient condition, we need to assume additional structure: we assume that the link of M Σ is a homogeneous space of positive scalar curvature, L = G / K , where the semisimple compact Lie group G acts transitively on L by isometries. Examples of such manifolds include compact semisimple Lie groups and Riemannian symmetric spaces of compact type. Under these assumptions, when M Σ and β M are spin, we reinterpret our obstruction in terms of two α -classes associated to the resolution of M Σ , M , and to the singular locus β M. Finally, when M Σ , β M , L and G are simply connected and dim M is big enough, and when some other conditions on L (satisfied in a large number of cases) hold, we establish the main result of this paper, showing that the vanishing of these two α -classes is also sufficient for the existence of a well-adapted wedge metric of positive scalar curvature.
- Subjects
SEMISIMPLE Lie groups; LOCUS (Mathematics); CURVATURE; SYMMETRIC spaces; HOMOGENEOUS spaces; RIEMANNIAN manifolds
- Publication
Journal of Topology & Analysis, 2023, Vol 15, Issue 2, p413
- ISSN
1793-5253
- Publication type
Article
- DOI
10.1142/S1793525321500333