Timeline for Quick definition of the tangent space
Current License: CC BY-SA 3.0
3 events
| when toggle format | what | by | license | comment | |
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| May 21, 2012 at 21:34 | comment | added | Pietro Majer | More formally, if $\mathcal{A}_x$ is the local atlas of $M$ at $x$, we define $\left( T _ x M, \{ d\phi(x) \} _ {\phi\in\mathcal{A} _ x}\right)$ as the limit cone of the diagram of the differentials of the transition maps at $x$, i.e. the linear isomorphisms $d(\psi\phi^{-1})(\phi(x))$. This notation is consistent with the chain rule of differentiation, for $d(\psi\phi^{-1})(\phi(x))d\phi(x)= d\psi(x)$. | |
| May 21, 2012 at 20:32 | comment | added | Dylan Moreland | But we need to place some equivalence relation on these things, right? Or is there a way of avoiding this? | |
| May 21, 2012 at 19:44 | history | answered | JHM | CC BY-SA 3.0 |