Timeline for Homotopy groups of smooth manifolds?
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
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| Apr 21 at 2:37 | comment | added | Ryan Budney | @PaulMeier: I was talking about the 3-dimensional case, at that point. | |
| Mar 18, 2015 at 16:19 | comment | added | Andreas Thom | @PaulMeier: It is not true that $\pi_2$ is always finitely generated, see A. Dimca, S. Papadima, A. Suciu, Non-finiteness properties of fundamental groups of smooth projective varieties. J. Reine Angew. Math. 629 (2009), 89–105. | |
| Oct 12, 2012 at 13:45 | comment | added | Paul Meier | A bit offtopic, but I would like to know why pi_2 of a compact manifold is always finitely generated as module over pi_1? (One knows that this is not true for an arbitrary finite CW-complex.) | |
| Jan 10, 2010 at 0:02 | vote | accept | Ilya Nikokoshev | ||
| Jan 9, 2010 at 21:43 | history | edited | Ryan Budney | CC BY-SA 2.5 |
adapt to new statement of the question
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| Jan 9, 2010 at 21:14 | history | edited | Ryan Budney | CC BY-SA 2.5 |
moved my comment into response, to TeX it up
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| Jan 9, 2010 at 21:02 | history | edited | Ryan Budney | CC BY-SA 2.5 |
TeX it up
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| Nov 17, 2009 at 0:40 | comment | added | Ryan Budney | There are some natural K(pi,1) manifolds, but they seem to be a very sparse family among manifolds. Once you get beyond dimension 3 I'd suspect non-positively curved manifolds are extremely rare. For example, take a connect sum of n copies of CP^2. Those never have NPC metrics, and yet they represent oriented 4-manifolds up to cobordism. Are there any good theorems about how NPC metrics relate to cobordism, Stiefel-Whitney and Pontriagin numbers? I would guess NPC manifolds represent a very sparse sub-ring of the oriented cobordism ring. | |
| Nov 17, 2009 at 0:19 | comment | added | Tom Church | But compact boundaryless manifolds are quite often Eilenberg-Maclane spaces, for example any manifold with a non-positively curved Riemannian metric. | |
| Nov 16, 2009 at 23:23 | history | edited | Ryan Budney | CC BY-SA 2.5 |
tweak
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| Nov 16, 2009 at 23:13 | history | edited | Ryan Budney | CC BY-SA 2.5 |
small tweak
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| Nov 16, 2009 at 23:07 | history | answered | Ryan Budney | CC BY-SA 2.5 |