Timeline for Topology of function spaces?
Current License: CC BY-SA 2.5
7 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2011 at 20:07 | vote | accept | José Figueroa-O'Farrill | ||
| Aug 11, 2010 at 18:28 | comment | added | Ryan Budney | Regarding your last sentence, a reference is Henderson and West "Triangulated infinite-dimensional manifolds" Bull AMS 76 (1970) 655--660. i.e. these mapping spaces have the homotopy-type of CW-complexes. | |
| Aug 11, 2010 at 18:16 | comment | added | Igor Belegradek | One small correction: the identification of $\pi_k(C^0(\Sigma, G))$ and $[S^k\times\Sigma, G]$ is only valid when $C^0(\Sigma, G)$ is path-connected, which is the case when $G$ is simply-connected compact Lie group, as any map from a surface to $G$ is null-homotopic. In general, a choice of basepoint $*$ in $C^0(\Sigma, G)$ picks up a subset in $[S^k\times\Sigma, G]$ corresponding to $\pi_k(C^0(\Sigma, G), *)$. | |
| Aug 11, 2010 at 14:57 | history | edited | Igor Belegradek | CC BY-SA 2.5 |
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| Aug 11, 2010 at 14:46 | history | edited | Igor Belegradek | CC BY-SA 2.5 |
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| Aug 11, 2010 at 13:18 | comment | added | José Figueroa-O'Farrill | Thanks, Igor. This Oberwolfach report is really interesting! I have added to the question some more information on the $X$ and $Y$ of most interest to me: $X$ a Riemann surface and $G$ a Lie group. | |
| Aug 11, 2010 at 1:28 | history | answered | Igor Belegradek | CC BY-SA 2.5 |