1
$\begingroup$

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!

Improve this question
$\endgroup$
2
  • 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! $\endgroup$
    – Dominic Petti
    Jun 4, 2020 at 19:55

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.