Timeline for Extending binary operation used by homotopy classes
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 1, 2014 at 22:57 | comment | added | Qiaochu Yuan | See ncatlab.org/nlab/show/fundamental+groupoid and ncatlab.org/nlab/show/path+groupoid. | |
| Apr 1, 2014 at 16:10 | comment | added | Jose Capco | Yes, indeed I don't see much to $*$ here. you can't assume associativity so it isn't strictly a semigroup. Though you can force associativity if you for instance require that $*$ concatenates the two paths by attaching the first path to the second path if the first path endpoint intersects the second path, so halfway thru you have the first path and the other halfway is a section of the second part starting from the first point of intersection of the first path endpoint to the second path (if this intersection exists). | |
| Apr 1, 2014 at 14:37 | answer | added | Ronnie Brown | timeline score: 2 | |
| Apr 1, 2014 at 13:04 | comment | added | Mark Grant | Your operation is only associative up to homotopy (perhaps you want to talk about end-point preserving homotopy classes of paths, in which case the fundamental groupoid may be a more natural object to study). The lack of symmetry here is a bit unsettling, too. You could alternatively get a partial monoid by declaring $p\ast q$ to be defined only when $p(1)=q(0)$. | |
| Apr 1, 2014 at 12:25 | history | asked | Jose Capco | CC BY-SA 3.0 |