Timeline for A generalized Thom Isomorphism
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 11, 2014 at 9:33 | comment | added | Liviu Nicolaescu | I used the term "ill posed" with a nod to math-phyz where it has a precise meaning. | |
| Mar 11, 2014 at 6:52 | comment | added | Mark Grant | @LiviuNicolaescu: I agree with you on some level. I was just trying to understand the sentence in your answer. (To me, it seems that what the OP proposed did work, even if it turned out to be trivial.) | |
| Mar 9, 2014 at 10:19 | comment | added | Liviu Nicolaescu | Also, I'm not opposed to the question. I think that it had an easy answer that could have picked up from even a superficial reading of the proof of Thom iso. | |
| Mar 9, 2014 at 10:11 | comment | added | Liviu Nicolaescu | As opposed to this question, the Thom isomorphism is a central part of a deep and far reaching phenomenon called duality. I know of two rather different ways duality was generalized: to the cohomology of arbitrary sheaves (Verdier) and to other cohomology theories. E.g. the Bott periodicity is a special case of Thom iso for K-theory. It corresponds to the case X= point. In all incarnations of Thom iso, the case X=point is fundamental. | |
| Mar 9, 2014 at 9:40 | comment | added | Mark Grant | @LiviuNicolaescu: Could you please explain your objection to the question? As far as I see it, Alex Degtyarev's answer describes what happens (even when $X$ is a point). The question has an easy answer, but one which I can imagine being useful to know, and it seems to be a genuine generalization of the Thom isomorphism. | |
| Mar 7, 2014 at 11:55 | comment | added | Liviu Nicolaescu | Then read csrefully any proof of the Thom isomorphism theorem to understand why your question is ill posed. | |
| Mar 7, 2014 at 0:05 | comment | added | Ali Taghavi | at this time the book is not available to me. do you remember a particular statment or proposition in the book related to my question? | |
| Mar 6, 2014 at 23:22 | comment | added | Liviu Nicolaescu | This question goes nowhere. Have a look at the book by Bott and Tu Differential forms in algebraic topology. | |
| Mar 6, 2014 at 23:10 | comment | added | Ali Taghavi | Yes the particular case X=point shows that the "right side" can not depend only on $X$, but it depend also on the number of deleted points. So i am trying to underestand the first answer to my question.In fact my question: Does my propose leads to triviality? | |
| Mar 6, 2014 at 0:18 | review | Low quality posts | |||
| Mar 6, 2014 at 3:46 | |||||
| Mar 6, 2014 at 0:02 | history | answered | Liviu Nicolaescu | CC BY-SA 3.0 |