We define and study, under suitable assumptions, the fundamental class, the index class and the rho class of a spin Dirac operator on the regular part of a spin stratified pseudomanifold. More singular structures, such as singular foliations, are also treated. We employ groupoid techniques in a crucial way; however, an effort has been made in order to make this article accessible to readers with only a minimal knowledge of groupoids. Finally, whenever appropriate, a comparison between classical microlocal methods and groupoids methods has been provided.

Singular spaces, groupoids and metrics of positive scalar curvature / Piazza, P.; Zenobi, V. F.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 137:(2019), pp. 87-123. [10.1016/j.geomphys.2018.09.016]

Singular spaces, groupoids and metrics of positive scalar curvature

Piazza P.;Zenobi V. F.
2019

Abstract

We define and study, under suitable assumptions, the fundamental class, the index class and the rho class of a spin Dirac operator on the regular part of a spin stratified pseudomanifold. More singular structures, such as singular foliations, are also treated. We employ groupoid techniques in a crucial way; however, an effort has been made in order to make this article accessible to readers with only a minimal knowledge of groupoids. Finally, whenever appropriate, a comparison between classical microlocal methods and groupoids methods has been provided.
2019
Groupoids; positive scalar curvature; stratified spaces
01 Pubblicazione su rivista::01a Articolo in rivista
Singular spaces, groupoids and metrics of positive scalar curvature / Piazza, P.; Zenobi, V. F.. - In: JOURNAL OF GEOMETRY AND PHYSICS. - ISSN 0393-0440. - 137:(2019), pp. 87-123. [10.1016/j.geomphys.2018.09.016]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1469158
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