Timeline for Is there a homology theory that gives a *necessary and sufficient* condition for homotopy equivalence?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Apr 25, 2014 at 19:12 | comment | added | Qiaochu Yuan | When you say "isomorphic" and "an isomorphism" above you mean "quasi-isomorphic" and "a quasi-isomorphism" respectively since you're working with complexes and not their homology. | |
| Apr 23, 2014 at 9:19 | comment | added | Fernando Muro | @WlodzimierzHolsztynski I wouldn't say that's the goal of htpy theory, mostly because most algorithms in htpy theory are exponential, hence not useful for explicit computations. This is just my opinion, of course. | |
| Apr 22, 2014 at 22:00 | comment | added | Włodzimierz Holsztyński | @Fernando: Right. The goal of the homotopy theory is to obtain algorithms in the important special cases; often it's done, one way or another, via homology. | |
| Apr 22, 2014 at 20:47 | comment | added | Fernando Muro | @WlodzimierzHolsztynski Homotopy groups of CW-complexes with no 1-cells can be computed via an algorithm. | |
| Apr 22, 2014 at 13:52 | answer | added | Ronnie Brown | timeline score: 6 | |
| Apr 22, 2014 at 9:25 | answer | added | D.-C. Cisinski | timeline score: 14 | |
| Apr 21, 2014 at 16:41 | answer | added | Qiaochu Yuan | timeline score: 30 | |
| Apr 21, 2014 at 13:37 | comment | added | Eric Wofsey | What sort of "nonabelian homology" do you have in mind exactly? Most generalizations of homology that I know of do not come from any sort of complexes. | |
| S Apr 21, 2014 at 12:36 | history | suggested | Michał Kukieła | CC BY-SA 3.0 |
added missing word "equivalence" in "f is a homotopy equivalence"
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| Apr 21, 2014 at 12:33 | review | Suggested edits | |||
| S Apr 21, 2014 at 12:36 | |||||
| Apr 21, 2014 at 7:17 | comment | added | Włodzimierz Holsztyński | Homology is algorithmic while homotopy is not. At least that's the idea. | |
| Apr 21, 2014 at 7:11 | comment | added | Fernando Muro | Homology with local coefficient, see Whitehead's theorem. | |
| Apr 21, 2014 at 6:30 | comment | added | Allen Knutson | Start here: en.wikipedia.org/wiki/Rational_homotopy_theory | |
| Apr 21, 2014 at 6:14 | history | asked | geodude | CC BY-SA 3.0 |