Classifying spaces for families of subgroups

1 Introduction

Given a discrete group $G$$<!-- COMMENT: To achieve a unified layout, along with using the template below, please OBSERVE the following: besides, $...$ and $$...$$, you should use two environments: - For statements like Theorem, Lemma, Definition etc., use e.g. {{beginthm|Theorem 1|(Milnor)}} ... ... ... {{endthm}}. - For references, use e.g. {{cite|Milnor1958b}}. END OF COMMENT --> == Introduction == <wikitex>; Given a discrete group $G$ and a family of subgroups $\mathcal{F}$ of $G$, there is a $G$-CW complex $E_\mathcal{F}G$ that classifies $G$-CW complexes with isotropy contained in $\mathcal{F}$. That is, for every $G$-CW complex $X$, there is a $G$-equivariant map $X \to E_\mathcal{F}G$ that is unique up to $G$-equivariant homotopy. {{beginthm|Definition (Family of Subgroups)|}} {{endthm}} </wikitex> == Construction and examples == <wikitex>; ... </wikitex> == Invariants == <wikitex>; ... </wikitex> == Classification/Characterization == <wikitex>; ... </wikitex> == Further discussion == <wikitex>; ... </wikitex> == References == {{#RefList:}} <!-- Please modify these headings or choose other headings according to your needs. --> [[Category:Manifolds]] {{Stub}}G$ and a family of subgroups $\mathcal{F}$$\mathcal{F}$ of $G$$G$, there is a $G$$G$-CW complex $E_\mathcal{F}G$$E_\mathcal{F}G$ that classifies $G$$G$-CW complexes with isotropy contained in $\mathcal{F}$$\mathcal{F}$. That is, for every $G$$G$-CW complex $X$$X$, there is a $G$$G$-equivariant map $X \to E_\mathcal{F}G$$X \to E_\mathcal{F}G$ that is unique up to $G$$G$-equivariant homotopy.

Definition (Family of Subgroups) 1.1.

2 Construction and examples

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3 Invariants

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4 Classification/Characterization

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5 Further discussion

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6 References

This page has not been refereed. The information given here might be incomplete or provisional.