Timeline for what does BG classify? i.e. what is a principal fibration?

5 events

when toggle format	what		by	license	comment
Dec 10, 2011 at 20:49	comment	added	Cary		OK, so in your setup, the answers are (1): all principal homogeneous spaces; (2): quasifibrations, Serre fibrations, Hurewicz fibrations, OR G-fibrations; (3): fiberwise maps commuting with the G-action. Using May's answer, anything in (2) with a fiberwise right G-action is (3)-equivalent to May's notion of G-fibration, which is classified up to (3)-equivalence by BG. We get the equivalence by applying Γ, essentially the usual trick for replacing maps by fibrations. So now we have four distinct classification problems that are all solved by BG.
Dec 9, 2011 at 21:58	history	edited	Tom Goodwillie	CC BY-SA 3.0	added 10 characters in body; deleted 10 characters in body
Dec 9, 2011 at 20:49	history	edited	Tom Goodwillie	CC BY-SA 3.0	deleted 15 characters in body
Dec 9, 2011 at 18:20	comment	added	Cary		Thank you! This is exactly what I'm looking for: some type of fibration/quasifibration with a fiberwise G-action, up to fiberwise maps commuting with this action. As I said, there's something similar to this in May's book. And you're also correct in guessing that I want to preserve G, or at least work with some monoid mapping into or out of G, rather than resorting to a zig-zag.
Dec 9, 2011 at 16:53	history	answered	Tom Goodwillie	CC BY-SA 3.0