Timeline for Classifying spaces
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 4, 2016 at 13:43 | comment | added | Sean Tilson | Have you looked at the Sullivan conjecture? | |
| Nov 3, 2016 at 14:52 | comment | added | Peter May | The action of $G$ on $EG$ must be free; omitted from your definition. | |
| Nov 3, 2016 at 9:15 | comment | added | Jens Reinhold | I once wrote some expository notes on classifying spaces which also conatin a list of references; maybe one day when I have a webpage I will also put them there... if you are interested in reading them, please contact me via jreinh AT stanford DOT edu | |
| Nov 3, 2016 at 8:02 | comment | added | HJRW | A discrete group with finite BG is said to be of type F. Many, many groups satisfy this property: all torsion-free hyperbolic groups, for instance. (But notice that they have to be finitely presentable.) | |
| Nov 3, 2016 at 7:08 | review | Close votes | |||
| Nov 3, 2016 at 8:51 | |||||
| Nov 3, 2016 at 6:53 | comment | added | YCor | Suggested references: Brown, Cohomology of groups. Geoghegan, Topological methods in group theory. | |
| Nov 3, 2016 at 6:36 | history | edited | Tom Ultramelonman | CC BY-SA 3.0 |
added 177 characters in body
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| Nov 3, 2016 at 6:29 | comment | added | Tom Ultramelonman | @OscarRandal-Williams Yes, I might have made an error when composing my question. When I say finite, I mean the number of orbits by $G$ are finite. As such the better question would be, when is $BG$ finite or of finite type. I'll change the question! | |
| Nov 2, 2016 at 21:06 | comment | added | Alex Degtyarev | You should check group cohomology. | |
| Nov 2, 2016 at 20:48 | comment | added | Oscar Randal-Williams | What people usually mean by "classifying space" is the quotient $BG = (EG)/G$. What you have called $EG$ is never finite (unless $G$ is trivial): if $G$ has an element of finite order then $EG$ must be infinite-dimensional; if $G$ is infinite then $EG$ must have infinitely-many vertices. | |
| Nov 2, 2016 at 20:46 | comment | added | Thomas Rot | Very few of these will be finite. Here is a list which contains some finite ones: mathoverflow.net/questions/56363/… . | |
| Nov 2, 2016 at 20:31 | history | asked | Tom Ultramelonman | CC BY-SA 3.0 |