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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2025
Автори: Puglisi, Massimiliano, Schick, Thomas, Zenobi, Vito Felice
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2025
Онлайн доступ: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
Цитувати: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

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Puglisi, Massimiliano
Schick, Thomas
Zenobi, Vito Felice
author_facet Puglisi, Massimiliano
Schick, Thomas
Zenobi, Vito Felice
citation_txt 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
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description 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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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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last_indexed 2026-03-20T17:42:27Z
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publisher Інститут математики НАН України
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spelling Puglisi, Massimiliano
Schick, Thomas
Zenobi, Vito Felice
2026-02-20T07:59:38Z
2025
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
1815-0659
2020 Mathematics Subject Classification: 57R91; 57R90; 53C27; 53C21
arXiv:2412.07955
https://nasplib.isofts.kiev.ua/handle/123456789/214190
https://doi.org/10.3842/SIGMA.2025.093
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.
The authors thank the referees for the careful reading of the paper, improving the presentation, and helping to avoid inaccuracies.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
Article
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spellingShingle Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
Puglisi, Massimiliano
Schick, Thomas
Zenobi, Vito Felice
title Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
title_full Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
title_fullStr Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
title_full_unstemmed Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
title_short Stolz Positive Scalar Curvature Structure Groups, Proper Actions and Equivariant 2-Types
title_sort stolz positive scalar curvature structure groups, proper actions and equivariant 2-types
url https://nasplib.isofts.kiev.ua/handle/123456789/214190
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