Timeline for Alexander duality theorem
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 14, 2014 at 19:37 | review | Close votes | |||
| Dec 25, 2014 at 3:02 | |||||
| Mar 20, 2013 at 3:33 | comment | added | Misha | @Mark: The old-fashioned ("pre-cobordism-theory") convention is that empty set has topological dimension $-1$: This convention is most suitable for the purposes of separation theorems, like the one in the current question. | |
| Mar 20, 2013 at 1:13 | comment | added | Hiro Lee Tanaka | The definition of orientability is another matter--in cobordism theory for orientable manifolds, the two possible conventions are both strange: Either the empty manifold has a unique orientation, (any orientable manifold should have two!) or the empty manifold can be formally given two different orientations whilst the empty cobordism between them realizes an isomorphism. (When is an orientable manifold invertibly cobordant to its opposite?) | |
| Mar 18, 2013 at 19:11 | vote | accept | Amir | ||
| Mar 18, 2013 at 13:44 | comment | added | Mark Grant | @Steven: The empty set is a manifold of any dimension (this convention being forced onto those of us who use bordism groups). | |
| Mar 18, 2013 at 2:45 | comment | added | Steven Landsburg | Ryan: Normally the word "hypersurface" implies codimension 1, no? | |
| Mar 17, 2013 at 20:28 | answer | added | Dan Petersen | timeline score: 6 | |
| Mar 17, 2013 at 20:20 | comment | added | Ryan Budney | No, for example, if $\Sigma$ is the empty set then the complement has only one component. Have you tried looking up the Jordan-Brouwer separation theorem? | |
| Mar 17, 2013 at 19:55 | history | asked | Amir | CC BY-SA 3.0 |