Timeline for Cap product à la Poincaré
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 17, 2014 at 21:03 | comment | added | ARG | Many thanks for the references! As for the choice of words, the first time cup product was presented to me, it was branded as exteremely unrigorous and dangerous to see it (dually) as an intersection. This and the fact that I always saw cup being used and never intersection fueled my unjustified belief in it being ill-defined. I guess that transversality hypothesis make intersection product more cumbersome than cup... | |
| Dec 17, 2014 at 20:44 | comment | added | Allen Hatcher | Also, $T^*$ is a cellulation (a decomposition into cells), not a triangulation as stated in the question. | |
| Dec 17, 2014 at 20:42 | comment | added | Allen Hatcher | You are talking about a product that involves just homology and not cohomology, so this is not the cap product. Instead it is usually called the intersection product. A classical reference for the intersection product is the textbook by Seifert and Threlfall. A more recent textbook source is Bredon's "Topology and Geometry". Bredon attributes the intersection product to Lefschetz. The intersection product is a perfectly well-behaved product, with the right hypotheses, so it's not clear why you use the words "evil", "fails", and "ill-defined" in reference to it. | |
| Dec 17, 2014 at 16:19 | vote | accept | ARG | ||
| Dec 17, 2014 at 13:43 | answer | added | David E Speyer | timeline score: 5 | |
| Dec 17, 2014 at 12:34 | history | asked | ARG | CC BY-SA 3.0 |