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May 15, 2012 at 17:30 vote accept Nicolas Schmidt
May 15, 2012 at 17:30 comment added Nicolas Schmidt Nice answer, I was hoping for something along these lines. Could you explain why properness is necessary for existence of slices? I mean we only have a local condition on the action (which implies properness, locally), but a locally proper group action need not be proper. Regarding the terminology: Many people take principal $G$-bundles to be locally trivial, but many don't (e.g. Husemöller).
May 15, 2012 at 15:40 history edited Misha CC BY-SA 3.0
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May 15, 2012 at 15:28 history edited Misha CC BY-SA 3.0
added 160 characters in body
May 15, 2012 at 15:15 history answered Misha CC BY-SA 3.0