Timeline for Is an algebraic geometer's fibration also an algebraic topologist's fibration?
Current License: CC BY-SA 2.5
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 27, 2010 at 15:42 | vote | accept | HYYY | ||
| Jun 15, 2010 at 6:19 | comment | added | Andrew Stacey | I'm voting to close because the questioner has not added any clarification. As posed, it is incredibly difficult to work out what would make a good answer to this question. | |
| Jun 15, 2010 at 0:37 | history | edited | Tim Perutz | CC BY-SA 2.5 |
More descriptive title; added AG tag
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| Jun 15, 2010 at 0:34 | answer | added | Tim Perutz | timeline score: 5 | |
| Jun 15, 2010 at 0:13 | comment | added | David Roberts♦ | Not to mention Dold fibrations or quasifibrations. And depending on how far you define alg-top, Quillen fibrations (these live in Cat and geometrically realise to quasifibrations, by the lemma to Theorem B) | |
| Jun 14, 2010 at 23:00 | comment | added | HYYY | Thanks,Tim Perutz. I always assume it should be the definition of fibration in standard algebraic topology (the homotopical fibration as you mentioned) | |
| Jun 14, 2010 at 22:26 | comment | added | Tim Perutz | Boyarksy: probably so. I was careless and didn't specify source and target of the morphism (for a Lefschetz fibration, both are non-singular and the target is a curve). I was thinking of the convention in Barth et al., "Compact complex surfaces", p. 110, which seems to be that a fibration on a non-singular, connected complex surface is a proper, surjective, holomorphic map to a non-singular curve. | |
| Jun 14, 2010 at 22:00 | comment | added | Boyarsky | @Tim: probably also should always include flatness to get a handle on decent properties, right? For example, blow-up at a point is presumably not a reasonable notion of "fibration" in any circumstance, whereas any proper surjective map between smooth connected schemes or analytic spaces of pure dimension is automatically flat (and hence falls into this notion of fibration). For example, such "fibrations" have sections over a finite flat cover locally on the base. Lefschetz fibrations are also flat. | |
| Jun 14, 2010 at 21:15 | comment | added | Tim Perutz | In complex analytic or algebraic geometry, "fibration" sometimes simply means "proper, surjective morphism". For instance, a "Lefschetz fibration" is a fibration with non-degenerate critical points and distinct critical values. This usage has nothing to do with homotopical usage. The critical fibres of a Lefschetz fibration have different homotopy types to the regular fibres, so a LF with at least one critical point is not a Hurewicz fibration (nor a Serre fibration, for that matter). | |
| Jun 14, 2010 at 21:05 | comment | added | Andrew Stacey | Please add some context, such as a paper where you have seen this, and perhaps an example of what you've seen for XXX. Also please say what algebraic topology you already know (do you know the difference between a Serre fibration and a Hurewicz fibration, for example?). | |
| Jun 14, 2010 at 20:46 | history | asked | HYYY | CC BY-SA 2.5 |