Timeline for cohomology ring of infinite iterated loop space
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 5, 2015 at 12:47 | comment | added | user43326 | No, in homology there are not only the elements $Q^I(\iota _n)$'s but their products. And they are not primitive. | |
| Sep 5, 2015 at 12:44 | comment | added | QSR | Dear Prof., you mentioned that "since the fundamental class is primitive, so all the classes obtained by Dyer-Lashof operations are primitive as well". But if this is true for the homology, the cup product of cohomology would be trivial. | |
| Sep 3, 2015 at 14:47 | comment | added | user43326 | The first fact is the consequence of the fact that $\Omega ^{\infty}$ is a right adjoint, the second, as is explained, follows from the fact that all polynomial generators of $H_*(QS^n)$ with $n>0$ are primitive. I presume you can find all of these (except the first one ) in somewhere section 3 of Wellington's book, but unfortunately I don't have it on the hand. | |
| Sep 3, 2015 at 14:36 | history | edited | user43326 | CC BY-SA 3.0 |
Added a detailed proof.
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| Sep 3, 2015 at 12:47 | comment | added | QSR | Thanks, Prof. Could you explain more? Which page could I find the results? | |
| Sep 3, 2015 at 12:34 | vote | accept | QSR | ||
| Sep 3, 2015 at 12:43 | |||||
| Sep 3, 2015 at 12:28 | history | answered | user43326 | CC BY-SA 3.0 |