Timeline for Infinite loop space structure of $BU^+$
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| Apr 18, 2012 at 18:55 | comment | added | Peter May | Do you really mean ``commute''? In any case, probably the closest thing would be to understand moduli spaces of infinite loop structures (there is relevant spectrum level work of Goerss and Hopkins). By way of example, there is a beautiful but very special case where there is an answer: Adams and Priddy proved that BSU and BSO have unique infinite loop structures (whereas BU and BO do not: $\oplus$ and $\otimes$ give inequivalent infinite loop structures) | |
| Apr 18, 2012 at 12:12 | comment | added | berl13 | That's very interesting, so another question arises for me. Perhaps it leaves the frame of this question. But do you know if there are any standard techniques to compare infinite loop space structures on the same space. More precisely, the situation is the following. One has a space $X$ which is an infinite loop space w.r.t. two infinite loop spaces structures and the corresponding multiplications on its zero component commute. Are there tools to say to which extent the structures differ. I have an example in mind where I am pretty sure that they are not the same. | |
| Apr 18, 2012 at 2:40 | history | answered | Peter May | CC BY-SA 3.0 |