Positive scalar curvature on spin pseudomanifolds: the fundamental group and secondary invariants. (English) Zbl 1518.57036
The authors continue the program started in [the first author, Geom. Topol. 5, 683–718 (2001; Zbl 1002.57055)] and further developed in recent papers [the first author and third author, “Positive scalar curvature on manifolds with fibered singularities”, Preprint, arXiv:1808.06007; the authors, “Positive scalar curvature on simply connected spin pseudomanifolds”, Preprint, arXiv:1908.04420] for the study of Thom-Mather pseudomanifolds of depth one.
They define a metric adapted to the singularity structure on manifolds with fibered singularities and study obstructions to positive scalar curvature.
In particular, they study fibered pseudomanifolds, Spin bordism of geometric Witt pseudomanifolds, \(C^*\)-algebras and KO-classes associated with a wedge differential operator, relevant surgery and bordism theorems.
At the end of the paper, the authors present open problems and topics for further study.
They define a metric adapted to the singularity structure on manifolds with fibered singularities and study obstructions to positive scalar curvature.
In particular, they study fibered pseudomanifolds, Spin bordism of geometric Witt pseudomanifolds, \(C^*\)-algebras and KO-classes associated with a wedge differential operator, relevant surgery and bordism theorems.
At the end of the paper, the authors present open problems and topics for further study.
Reviewer: Malkhaz Bakuradze (Tbilisi)
MSC:
| 57R15 | Specialized structures on manifolds (spin manifolds, framed manifolds, etc.) |
| 53C27 | Spin and Spin\({}^c\) geometry |
| 19L41 | Connective \(K\)-theory, cobordism |
| 55N22 | Bordism and cobordism theories and formal group laws in algebraic topology |
| 57R90 | Other types of cobordism |
Citations:
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