Timeline for When is the classifying space of a group/H-space rationally equivalent to a product of Eilenberg-MacLane spaces?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 9 at 20:15 | comment | added | Tyrone | @ThorbenK the rational $A_\infty$-equivalence will push down to the classifying space. | |
| Mar 9 at 19:19 | comment | added | LSpice | @RyanBudney, re, thanks! I see the author got it. | |
| Mar 9 at 18:37 | comment | added | ThorbenK | @Tyrone but does it suffice that the group has a free graded commutative cohomology ring over the rationals? Does this push down to the classifying space? | |
| Mar 9 at 11:38 | comment | added | Tyrone | It will be true of any topological group (or even space) whose rational cohomology is a free associative, graded-commutative algebra over $\mathbb{Q}$. Simply choose a set of primitive generators to obtain a rational equivalence with a product of EM spaces. It's easy to verify that the obstructions for this to be an $A_\infty$-equivalence vanish. On the other hand, these cohomological conditions clearly need to hold for the outcome to be true. They're satisfied, for instance, by any group homotopy equivalent to a finite CW complex (e.g. any Lie group, as you recognise). | |
| Mar 9 at 7:55 | history | edited | ThorbenK | CC BY-SA 4.0 |
edited title
|
| Mar 9 at 6:46 | comment | added | Ryan Budney | @LSpice: you missed the title. | |
| Mar 8 at 21:31 | comment | added | Dave Benson | I believe it was for the sake of his first wife, Dorothy Jones, who found it easier to type it with a space. | |
| Mar 8 at 21:20 | comment | added | LSpice | Someone explained to me, but I can't remember the details of, the orthography of Mac Lane's name; he latterly went by Mac Lane, but originally by MacLane. (Maybe that's all there is to the explanation, but I seem to remember more.) But it was never Maclane, so I edited accordingly. | |
| Mar 8 at 21:19 | history | edited | LSpice | CC BY-SA 4.0 |
Maclane -> MacLane
|
| Mar 8 at 20:21 | history | edited | ThorbenK | CC BY-SA 4.0 |
added 2 characters in body
|
| Mar 8 at 19:53 | history | edited | ThorbenK | CC BY-SA 4.0 |
added 84 characters in body
|
| Mar 8 at 19:36 | history | asked | ThorbenK | CC BY-SA 4.0 |