Timeline for Is there a "unique" homogeneous contact structure on odd-dimensional spheres?
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7 events
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| Jun 26, 2014 at 15:01 | comment | added | Oldřich Spáčil | @BenoîtKloeckner Oh, I see, I misunderstood your comment. The B-E-M overtwisted object seems to be "the" analogue of the classical overtwisted disc in the sense that its existence ensures topological classification of overtwisted contact structures, i.e. two contact structures admitting the same B-E-M object are isotopic if and only if the underlying almost contact structures are homotopic. This is the viewpoint I had in mind when writing "only very recently". Of course, it might happen that for example the plastikstufe is an object equivalent to the B-E-M object, but that I don't know. | |
| Jun 26, 2014 at 10:02 | comment | added | Benoît Kloeckner | @OldřichSpáčil: i read the introduction of this paper too, but that the given notion is stronger than preceding ones does not mean that it is the first time such an analogue has been defined (or discovered), right? | |
| Jun 26, 2014 at 7:18 | comment | added | Giovanni Moreno | @OldřichSpáčil : I did not know this overtwisted/tight dichotomy - thank you for pointing it out. I'm going to give a look at the references you've suggested! | |
| Jun 25, 2014 at 23:31 | comment | added | Oldřich Spáčil | @BenoîtKloeckner Quoting from the B-E-M paper, page 3: "We note that there were many proposals for defining the overtwisting phenomenon in dimension greater than three. We claim that our notion is stronger than any other possible notions, in the sense that any exotic phenomenon, e.g. a plastikstufe, can be found in any overtwisted contact manifold." | |
| Jun 25, 2014 at 18:44 | comment | added | Benoît Kloeckner | Concerning overtwisted higher-dimensional contact structure, there is also a much earlier proposition by Klaus Niederkrüger (the plastikstufe replacing the overtwisted disk, no superseeded by the notion of a bLob). | |
| Jun 25, 2014 at 17:54 | comment | added | Oldřich Spáčil | I'll try to polish this answer later... | |
| Jun 25, 2014 at 17:51 | history | answered | Oldřich Spáčil | CC BY-SA 3.0 |