Talk:Ambient isotopy

Bulk of teensy "article" is wrong
About 85% of the article is as follows:

"In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an "ambient space", a manifold, taking a submanifold to another submanifold. For example in knot theory, one considers two knots the same if one can distort one knot into the other without breaking it. Such a distortion is an example of an ambient isotopy. More precisely, let N and M be manifolds and g and h be embeddings of N in M. The map is defined to be an ambient isotopy taking g to h if F0 is g, F1 is h and Ft induces and in addition, every  must induce a self homeomorphism of M.

The first sentence is correct. The second sentence illustrates something that is (at least on the surface) quite different, contrary to the fourth sentence. The fifth and sixth (= last) sentences above contain a mathematically meaningless passage:

"More precisely, let N and M be manifolds and g and h be embeddings of N in M. The map is defined to be an ambient isotopy taking g to h if F0 is g, F1 is h . . .."

I guess whoever wrote this doesn't know the concept of restricting a map to a smaller domain. If the language of restricted domains were used, this passage would be correct.

(The second and third sentences would still need to be fixed.)Daqu (talk) 06:02, 7 July 2008 (UTC)