# Talk:Normal bundle

Active discussions
WikiProject Mathematics (Rated Start-class, Low-priority)

## 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[1], as opposed to a "submanifold of ${\displaystyle \mathbb {R} ^{n}}$ ", 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

1. ^ W., Weisstein, Eric. "Abstract Manifold". mathworld.wolfram.com. Retrieved 2018-03-01.

## Conormal bundle

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