Timeline for Mapping class group of certain 3-manifolds
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 9, 2017 at 11:22 | vote | accept | Daniele Zuddas | ||
| Jun 9, 2017 at 0:36 | comment | added | Allen Hatcher | The theorem that diffeomorphisms of $M$ can be isotoped to take fibers to fibers is a special case of a theorem of Waldhausen in a two-part paper on graph manifolds in Inventiones 3-4 (1967-68). He worked in the PL category but the proof applies also in the smooth category if one uses Cerf's theorem that $\pi_0{\rm Diff}_+(S^3)=0$. Another classical exposition is in Jaco's Lectures on Three-Manifold Topology (1980), Theorem VI.18, which gives the analogous result for Seifert manifolds with non-empty boundary, leaving the closed case as an exercise (using similar methods). | |
| Jun 8, 2017 at 6:54 | comment | added | Daniele Zuddas | I understand, thank you! Yes, orientability of $M$ and orientation-preserving homeomorphisms are what I was thinking about. | |
| Jun 8, 2017 at 4:20 | history | edited | Allen Hatcher | CC BY-SA 3.0 |
added 226 characters in body
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| Jun 8, 2017 at 4:04 | history | answered | Allen Hatcher | CC BY-SA 3.0 |