Timeline for Space of embeddings of an $n$-ball into an $n$-manifold
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Oct 29, 2013 at 1:10 | comment | added | Lars | @OscarRandal-Williams : Thanks for the reference! | |
| Oct 29, 2013 at 1:09 | comment | added | Lars | @RicardoAndrade : Thank you very much for the references. They are very helpful. And if you do have the time, any further details would be very welcome. | |
| Oct 28, 2013 at 22:29 | comment | added | Ricardo Andrade | Regarding your second question: In particular, Oscar's reference and the ones I give above show that the map $\psi$ is locally trivial, i.e. a fibre bundle. So the contractibility of the fibres implies that the map is a homotopy equivalence. This implication uses the paracompactness of the base space, and follows from results of Dold and tom Dieck: see theorem 13.3.3 of tom Dieck's book "Algebraic topology". | |
| Oct 28, 2013 at 22:28 | comment | added | Ricardo Andrade | Here are a couple of references with a few details of a proof for the result you seek. 1. See theorem V.4.5 in my thesis at arxiv.org/abs/1210.7909 which actually deals with the case of multiple balls (be careful that the target space is mistyped for the case of more than one ball). This gives a very brief proof sketch that $\psi$ is locally trivial and a homotopy equivalence. 2. See also proposition 6.4 in arxiv.org/abs/1307.0322 which deals with the case of a single ball. | |
| Oct 28, 2013 at 22:18 | comment | added | Oscar Randal-Williams | For 2, see page 318 of ``Topologie de certains espaces de plongements" by J. Cerf. | |
| Oct 28, 2013 at 19:44 | review | First posts | |||
| Oct 28, 2013 at 19:49 | |||||
| Oct 28, 2013 at 19:24 | history | asked | Lars | CC BY-SA 3.0 |