I am having trouble finding information on a definition in P. Hanham's PhD thesis paper. recall that given a discrete group $G$ a $G$-CW-complex $X$ is a CW-complex equipped with a topological $G$ action such that if $G$ acts on a cell in $X$ trivially, then $G$ acts on each point in said cell trivially. Hanham says a free $G$-CW-complex ($G$-CW-complex with trivial stabilizers) is said to be a model for $EG$ if $X/G$ is a $K(G,1)$ Eilenberg-Maclane space.

My question is, why $EG$? Is this just a definition or is there more that i can learn about this '$EG$'. Hanham says nothing more on the topic. I'm pretty sure there is something more to this but i am having difficulty finding this online. If someone could point me in the right direction, I would greatly appreciate it. Thanks in advance!

  • 4
    $\begingroup$ $EG$ is standard notation for the total space of a principal $G$-bundle. $\endgroup$
    – Mark Grant
    Jun 4, 2020 at 19:54
  • $\begingroup$ @MarkGrant Thank you! $\endgroup$ Jun 4, 2020 at 19:55


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