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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2025
Main Authors: Puglisi, Massimiliano, Schick, Thomas, Zenobi, Vito Felice
Format: Article
Language:English
Published: Інститут математики НАН України 2025
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/214190
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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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Summary: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.
ISSN:1815-0659