Timeline for Boundaries of smooth manifolds
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2013 at 9:08 | history | edited | Ricardo Andrade | CC BY-SA 3.0 |
slight changes to make question more readable
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| Jul 17, 2013 at 8:56 | answer | added | Daniel Moskovich | timeline score: 4 | |
| Mar 22, 2013 at 13:53 | comment | added | Misha | Robert: The 5-manifold can have any handles you like: Every manifold has handle decomposition with handles of all possible indices. Moreover, you can take your 5-manifold and form its connected sum with a closed 5-manifold of your choice. Did you read Milnor's book on Morse theory? | |
| Mar 22, 2013 at 10:42 | comment | added | Robert | Apologies for lack of clarity, I am particularly interested in the 4 dimensional case as stated but was wondering if anything was known in general. Mainly I was wondering if we could bound the degree of the handles for instance if I have a 4 manifold which has 0, 1, 2 and 4 handles which bounds a 5 manifolds can we say that the 5 manifold only has 1 and 2 handles or are there any examples where the 5 manifold requires 3 handles. For instance the case with $S^4$ where there are no 1, 2 or 3 handles we know that the 5 manifolds is in fact the 5 ball and so also has no 1,2 or 3 handles. | |
| Mar 22, 2013 at 3:39 | comment | added | Misha | Tom: You might be right, but then the only meaningful question I see is to get an upper bound on the number of handles needed to construct some N if some handle info about M is given. In any case, it is OP's responsibility to state the precise problem he/she has in mind. | |
| Mar 22, 2013 at 2:38 | comment | added | Tom Goodwillie | Maybe the intended question was not about every N but about some N. | |
| Mar 21, 2013 at 22:07 | history | edited | Ricardo Andrade |
edited tags
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| Mar 21, 2013 at 15:18 | comment | added | Misha | Handle decomposition of N will be more complicated than the one of M. In order to formulate a better question, think about the case when M is the sphere and N is an arbitrary close n+1 manifold with a disk removed. | |
| Mar 21, 2013 at 12:09 | history | asked | Robert | CC BY-SA 3.0 |