Timeline for Computing homotopies
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 4, 2011 at 15:54 | comment | added | Tom Goodwillie | Not at all common, I'm sure. It was a special circumstance. | |
| Jan 4, 2011 at 15:13 | comment | added | Harry Gindi | @Tom: I wonder how common that is. | |
| Jan 4, 2011 at 14:39 | comment | added | Mariano Suárez-Álvarez | @Harry: you have a very weird concept of cheating if you think that specifying continuous functions at the point-set level feels like cheating! | |
| Jan 4, 2011 at 14:30 | comment | added | Tom Goodwillie | A topologist who will remain nameless once proudly told me of writing down a certain homotopy in a certain explicit way in order to deliberately conceal the two-step process by which it had been created. This was in order to prevent a specific other topologist from generalizing the argument. | |
| Jan 4, 2011 at 14:11 | comment | added | Harry Gindi | Also, specifying continuous functions at the point-set level feels like cheating and doesn't generalize well to other contexts (even simplicial sets). Are you aware of any homotopies appearing in important theorems for which there is only a point-set description? | |
| Jan 4, 2011 at 14:05 | comment | added | Harry Gindi | Yeah, I realize that was an "abuse of terminology", and you did understand what I was trying to get at. There is a canonical (in a certain sense) "description" of the homotopy by another one of its uses. In general, it's substantially easier to understand what's going on with homotopies if you can give descriptions of them in terms of other maps that you're already working with. That is, I think it's preferable to make homotopies out of other homotopies rather than write them down explicitly. Somehow this seems quite a bit more enlightening. | |
| Jan 4, 2011 at 13:54 | history | answered | Tom Goodwillie | CC BY-SA 2.5 |