Orbifolds, orbispaces and global homotopy theory

Juran, Branko

doi:10.2140/agt.2025.25.5175

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Orbifolds, orbispaces and global homotopy theory

Branko Juran

Algebraic & Geometric Topology 25 (2025) 5175–5203

DOI: 10.2140/agt.2025.25.5175

Abstract

Given an orbifold, we construct a global spectrum representing its stable global homotopy type. Global spectra now represent orbifold cohomology theories which automatically satisfy certain properties such as additivity and the existence of Mayer–Vietoris sequences. Moreover, the value at a global quotient orbifold $M ∕ ∕ G$ can be identified with the $G$ -equivariant cohomology of the manifold $M$ . Examples of orbifold cohomology theories which are represented by global spectra include Borel and Bredon cohomology theories and orbifold $K$ -theory. This also implies that these cohomology groups are independent of the presentation of an orbifold as a global quotient orbifold.

Keywords

orbifold cohomology, global homotopy theory

Mathematical Subject Classification

Primary: 55N32, 55P91

References

Publication

Received: 7 July 2020

Revised: 31 December 2024

Accepted: 10 January 2025

Published: 18 December 2025

Authors

Branko Juran
Department of Mathematical Sciences University of Copenhagen Copenhagen Denmark

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Volume 25, issue 9 (2025)