Talk:Normal bundle

Abstract manifold

The paragraph on stable normal bundles starts off with "Abstract manifolds...". It seems to me that this should be rephrased along the lines of "Generally, manifolds...". Or am I missing something here? Are abstract manifolds a thing? 77.250.56.167 (talk) 17:17, 25 July 2013 (UTC)

"Abstract manifold" is just a synonym of manifold when one wants to emphasise that there is no a priori given embedding into an affine space, as opposed to a "submanifold of $\mathbb {R} ^{n}$", for example. At the moment "abstract" is linked to abstraction while "manifold" is linked to manifold, which makes no sense to me; so I'm linking "abstract manifold" to abstract manifold which correctly redirects to manifold. In this way the subsequent comment "only an embedding (or immersion) of a manifold in another yields a normal bundle" becomes sensible. Ale.rossi91 (talk) 12:46, 1 March 2018 (UTC)

References

Conormal bundle

"and the ideal sheaf is locally generated by $x_{1},\dots ,x_{k}$". Maybe I'm wrong; but don't we mean $x_{k+1},\dots ,x_{n}$ ? 2A02:8071:B69E:9300:5471:1A9E:8287:91F8 (talk) 10:58, 2 February 2019 (UTC)