Timeline for Is the meaning of "irreducible manifold", "not reducible to other manifold"?
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 4, 2021 at 15:01 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 4, 2021 at 13:07 | answer | added | C.F.G | timeline score: 2 | |
| Apr 21, 2021 at 20:14 | comment | added | Ryan Budney | @C.F.G, correct. Symmetric spaces are an extremely structured family of manifolds. In particular (non-trivial) homotopy spheres are not symmetric spaces, I think this is an old result of Wu Chung Hsiang's, from the 60's. | |
| Apr 21, 2021 at 17:23 | comment | added | C.F.G | @RyanBudney: You said that in high dimensions irreducible manifolds do not exist. But I have seen many theorems contains "n-dimensional irreducible Riemannian symmetric spaces". Is this different from irreducible manifold? | |
| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
|
|
| Nov 28, 2019 at 21:59 | history | edited | Pietro Majer | CC BY-SA 4.0 |
grammar
|
| Nov 28, 2019 at 21:01 | comment | added | LSpice | What does it mean to ask what a word means, if not its definition? Are you looking for intuition? | |
| Nov 28, 2019 at 20:54 | comment | added | Ryan Budney | These are the theorems of Kervaire and Milnor from the early 60's. Do a Google or library search for "Groups of homotopy spheres" and you should find papers by those two. A significant portion of that work is summarized in Kosinski's "Differential Manifolds" book, as well. | |
| Nov 28, 2019 at 20:47 | comment | added | C.F.G | @RyanBudney: where can I find the proof of your (last) statement(s)? | |
| Nov 28, 2019 at 20:17 | comment | added | Ryan Budney | Regarding high dimensions, generally irreducible manifolds do not exist, this is because the connect-sum operation has some invertible objects -- in dimension 5 and up they are known as homotopy-spheres. | |
| Nov 28, 2019 at 19:05 | comment | added | Kevin Casto | The basic point is that you can write a non-prime manifold as a nontrivial connected sum; this is the sense in which it can be reduced. For 3-manifolds, prime and irreducible are equivalent except for two examples. Wikipedia says: 'From an algebraist's perspective, prime manifolds should be called "irreducible"''. | |
| Nov 28, 2019 at 18:39 | history | edited | C.F.G | CC BY-SA 4.0 |
added 116 characters in body; edited tags
|
| Nov 28, 2019 at 18:14 | history | asked | C.F.G | CC BY-SA 4.0 |