Timeline for Relation between different definitions of homotopy
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 26, 2016 at 6:10 | answer | added | skd | timeline score: 1 | |
| Nov 11, 2016 at 7:05 | comment | added | Tim Porter | Steven: your `more-or-less the same' could be misleading as you added going to the abelian simplicial group and that transition destroys a lot of information, i.e. the difference between homotopy and homology. | |
| Nov 10, 2016 at 17:43 | answer | added | Tim Porter | timeline score: 3 | |
| Nov 10, 2016 at 17:30 | comment | added | Denis Nardin | While Dold-Kan is a very good way to see that the definition of homotopy between chain complexes is a sensible one, it bears remember that a "homotopy" is in a sense part of the definition of your category. You might as well ask why the definition of maps of complexes and maps of topological spaces differ. | |
| Nov 10, 2016 at 17:06 | comment | added | Steven Landsburg | A chain complex of abelian groups is the same thing as an abelian simplicial group under the Dold-Kan correspondence. A topological space is more or less the same thing as an abelian simplicial group under the adjunction that takes a space to its singular complex and a simplicial object to its geometric realization. Now check what happens to homotopic maps of spaces as you translate them to maps of chain complexes and vice versa. | |
| Nov 10, 2016 at 16:59 | review | First posts | |||
| Nov 10, 2016 at 17:08 | |||||
| Nov 10, 2016 at 16:54 | history | asked | p-tow | CC BY-SA 3.0 |