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We introduce the notion of G∞–ring spectra. These are globally equivariant homotopy types with a structured multiplication, giving rise to power operations on their equivariant homotopy and cohomology groups. We illustrate this structure by analyzing when a Moore spectrum can be endowed with a G∞–ring structure. Such G∞–structures correspond to power operations on the underlying ring, indexed by the Burnside ring. We exhibit a close relation between these globally equivariant power operations and the structure of a β–ring, thus providing a new perspective on the theory of β–rings.
Stahlhauer, Michael 1
@article{10_2140_agt_2023_23_87,
author = {Stahlhauer, Michael},
title = {G\ensuremath{\infty}{\textendash}ring spectra and {Moore} spectra for \ensuremath{\beta}{\textendash}rings},
journal = {Algebraic and Geometric Topology},
pages = {87--153},
publisher = {mathdoc},
volume = {23},
number = {1},
year = {2023},
doi = {10.2140/agt.2023.23.87},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.87/}
}
TY - JOUR AU - Stahlhauer, Michael TI - G∞–ring spectra and Moore spectra for β–rings JO - Algebraic and Geometric Topology PY - 2023 SP - 87 EP - 153 VL - 23 IS - 1 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2023.23.87/ DO - 10.2140/agt.2023.23.87 ID - 10_2140_agt_2023_23_87 ER -
Stahlhauer, Michael. G∞–ring spectra and Moore spectra for β–rings. Algebraic and Geometric Topology, Tome 23 (2023) no. 1, pp. 87-153. doi: 10.2140/agt.2023.23.87
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