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arXiv · 1903.03152

A model structure via orbit spaces for equivariant homotopy

Mehmet Akif Erdal·Aslı Güçlükan İlhan
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Abstract

For a given group $G$ and a collection of subgroups $\mathcal F$ of $G$, we show that there exist a left induced model structure on the category of right $G$-simplicial sets, in which the weak equivalences and cofibrations are the maps that induce weak equivalences and cofibrations on the $H$-orbits for all $H$ in $\mathcal F$. This gives a model categorical criterion for maps that induce weak equivalences on $H$-orbits to be weak equivalences in the $\mathcal F$-model structure.

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Mehmet Akif Erdal, Aslı Güçlükan İlhan. 2019-03-07. A model structure via orbit spaces for equivariant homotopy. https://doi.org/10.1007/s40062-019-00241-4

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