Timeline for Fibration exact sequence in homotopy vs spectral sequence in (co)homology
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
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| May 10 at 15:26 | comment | added | John Palmieri | Homotopy groups are obtained by mapping out of a fixed space, cohomology groups are obtained by mapping into a fixed space. Fibration sequences behave well when mapped into (and cofibration sequences behave well when mapped out of). | |
| May 10 at 14:45 | comment | added | Fernando Muro | As I said, any relatively advanced monograph on algebraic topology is a possible source. I wonder, though, whether you want a mathematical source or a speculative one. I don't have a taste for the latter but many people seem to like them. The homotopy LES is very easy to construct and you've probably met it before. The total space of a fibration is a twisted cartesian product of the base and the fiber, its singular complex is a twisted tensor product, and such things have a SS, like bicomplexes. | |
| May 10 at 14:31 | comment | added | kindasorta | Thanks for your reply. I mean to ask if there is a certain particular reason that instead of having a fibration exact sequence in cohomology, there is a spectral sequence. What is the source for this asymmetry? | |
| May 10 at 14:06 | review | Close votes | |||
| May 21 at 3:07 | |||||
| May 10 at 13:53 | comment | added | Fernando Muro | What kind of answer are you looking for? Both 'sequences' are constructed in standard references on algebraic topology. You can easily follow their proofs if you have enough background. | |
| May 10 at 13:44 | history | asked | kindasorta | CC BY-SA 4.0 |