Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
In this note, we study equivariant versions of Stolz's -groups, the positive scalar curvature structure groups ˢᵖⁱⁿₙ()ᴳ, for proper actions of discrete groups . We define the concept of a fundamental groupoid functor for a -space, encapsulating all the fundamental group information of all the f...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/214190 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types. Massimiliano Puglisi, Thomas Schick and Vito Felice Zenobi. SIGMA 21 (2025), 093, 19 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | In this note, we study equivariant versions of Stolz's -groups, the positive scalar curvature structure groups ˢᵖⁱⁿₙ()ᴳ, for proper actions of discrete groups . We define the concept of a fundamental groupoid functor for a -space, encapsulating all the fundamental group information of all the fixed point sets and their relations. We construct classifying spaces for fundamental groupoid functors. As a geometric result, we show that Stolz's equivariant -group ˢᵖⁱⁿₙ()ᴳ depends only on the fundamental groupoid functor of the reference space . The proof covers, at the same time, in a concise and clear way, the classical non-equivariant case.
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| ISSN: | 1815-0659 |