Timeline for Homology versus cohomology of Lie groups
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 25, 2013 at 0:39 | comment | added | Jonathan Beardsley | Perhaps checkout Borel's Paper? ncbi.nlm.nih.gov/pmc/articles/PMC1063923/pdf/pnas01596-0040.pdf | |
| Jul 1, 2012 at 13:54 | answer | added | Peter May | timeline score: 5 | |
| Jun 30, 2012 at 13:27 | answer | added | Peter May | timeline score: 2 | |
| Jun 29, 2012 at 11:10 | comment | added | Lennart Meier | Indeed, I would call the product Vel explained the Pontryagin product (which is, more generally, defined for any H-space). | |
| Jun 29, 2012 at 9:43 | answer | added | Pierre | timeline score: 4 | |
| Jun 29, 2012 at 9:20 | comment | added | Chris Gerig | Also, there is the Pontryagin product in homology (under certain conditions). | |
| Jun 29, 2012 at 6:25 | comment | added | Bruce Westbury | The homology and cohomology of a Lie group are Hopf algebras. This example led Hopf to define Hopf algebras. | |
| Jun 29, 2012 at 6:12 | comment | added | Will Sawin | It's well-defined, since clearly a cycle-wthout boundary cross a cycle without boundary is a cycle without boundary, so you have a map on the chain complex, and $(\partial A)\times B=\partial (A\times B)$ as long as $\partial B$ is trivial, so it sends boundaries to boundaries. Then obviously the push-forward is also well-defined. | |
| Jun 29, 2012 at 5:57 | comment | added | Vidit Nanda | Of course, I have just realized that the cohomology cup product construction requires the Kunneth map also, since the cohomology of the product is not the product of the cohomology. I'm not sure how this translates into the "homology of Lie groups" setting though, so I will leave the question as it stands. | |
| Jun 29, 2012 at 5:48 | history | asked | Vidit Nanda | CC BY-SA 3.0 |