Re: help with math translation from French

Stephen J. Herschkorn wrote:
G. A. Edgar wrote:

In article <1183196056.612254.72190@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, gius
<giu.giorgi@xxxxxxxxx> wrote:



I ask you to translate the following paper of mathematics (it
consists in four lines) form French to English, please.


http://i7.tinypic.com/4uyknyu.jpg


V_n is an open set of M_{n+1}. The restriction of phi_n to V_n
is an embedding (immersion?) of an open set of M_{n+1} in E.
One applies this map to an embedding of M_{n+1} in E.
By applying the theorem of isotopy of a tubular neighborhood:
one applies the embedding to an embedding of a tubular neighborhood
of M_{n+1} in E of the sort in the following commutative
diagram:

I'm a little unsure about how to translate "plongement"
and "\'etand"---probably you need a topologist for that...


"etendre" ("étendre," but I don't know if the accented character will appear in a post) means " to extend." "One extends this map..."

Are "isotopy" and "tubular neighborhood" terms that one uses in English? I don't know the exact topic in topology here.

When I Google(tm) for web tools to help in such translations, I don't find anything completely satisfactory. Partially helpful are:

http://humanities.uchicago.edu/orgs/ARTFL/forms_unrest/FR-ENG.html and
http://www.math.unicaen.fr/~reyssat/dico/dicofa.html .



"tubular neighborhoods" appear in section 5 , page 17 here:
http://www.ms.unimelb.edu.au/~rubin/publications/smale.pdf

Maybe low-dimensional topology?


.

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