- #1

- 675

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Given a differentiable manifold

*M*. Denote the tangent space at [tex]p \in M[/tex] by [tex]T_p M[/tex]. Is the definition of the tangent bundle

[tex]TM = \lbrace (p, T_p M)|p \in M \rbrace[/tex]

or is it

[tex]TM = \lbrace (p, V)|p \in M , V \in T_p M\rbrace[/tex]?

Maybe I'm splitting hairs but there should be standard definition of one or the other, right?

I can discuss further why I think it matters but first let's just see if anyone is certain about the answer.