Timeline for Homology-Cohomology Pairing
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 11, 2012 at 0:13 | vote | accept | nerses | ||
| Aug 9, 2012 at 13:21 | comment | added | nerses | Yeah, I started suspecting something like this, when I was looking at $\mathrm{K}$ rationally. One can understand $K_\ast K\otimes \mathbb{Q}$ easily, so I wanted to understand $(K\wedge \mathbb{Q})^\ast(K\wedge \mathbb{Q})$ by just dualizing. This even ended up having elements that behaved much like the Adams operations. However, I could not recover the action of these operations on coefficient ring. I assume I made a mistake not taking into account these difference between left and right module structures. | |
| Aug 9, 2012 at 6:33 | answer | added | Mark Grant | timeline score: 5 | |
| Aug 9, 2012 at 0:45 | comment | added | Sean Tilson | the distinct left and right module structures definitely come in to play. They show up whenever you want to computations, look at a cobar resolution that would give you the ANSS. You can also think about it from a categorical viewpoint. The Hopf Algebroid you have is a cogroupoid object, one unit represents the source of a morphism, the other represents the target of a morphism. I believe Ravenel talks about this in one of his appendices to the "Green Book". | |
| Aug 8, 2012 at 22:37 | history | asked | nerses | CC BY-SA 3.0 |