Timeline for Diffeomorphisms vs homeomorphisms of 3-manifolds
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Dec 30, 2011 at 5:12 | history | edited | François G. Dorais |
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| Dec 29, 2011 at 19:35 | vote | accept | John Francis | ||
| Dec 29, 2011 at 19:26 | comment | added | Autumn Kent | (Sorry about my first answer. I got turned around.) | |
| Dec 29, 2011 at 19:24 | comment | added | John Francis | Here's one definition: let ${\sf Mfld}_3^{\sf sm}$ be the topological groupoid of smooth 3-manifolds with diffeomorphisms, and let ${\sf Mfld}_3$ be the topological one. Let $B$ be the classifying space functor. Then there is a natural map of spaces $$B{\sf Mfld}_3^{\sf sm} \longrightarrow B{\sf Mfld}_3.$$ One definition of the space of smooth structures on $M$ is that it is the homotopy fiber of this map, over the point $\{M\}$ in the base. One reference, for example, is Weiss & Williams' paper, Automorphisms of Manifolds. (This space is naturally a homotopy type , not a homeomorphism type.) | |
| Dec 29, 2011 at 19:22 | answer | added | Autumn Kent | timeline score: 26 | |
| Dec 29, 2011 at 19:16 | comment | added | Autumn Kent | What definition of "space of smooth structures" are you using? Shouldn't it just be a single point? | |
| Dec 29, 2011 at 18:08 | history | asked | John Francis | CC BY-SA 3.0 |