So I'm trying to learn about fibre bundles and I am looking at the example of a tangent bundle.(adsbygoogle = window.adsbygoogle || []).push({});

Given a differentiable manifoldM. 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.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Simple question about definition of tangent bundle

**Physics Forums | Science Articles, Homework Help, Discussion**