Editing Connection form (section)

====Global connection forms====
If {''U''<sub>''p''</sub>} is an open covering of ''M'', and each ''U''<sub>''p''</sub> is equipped with a trivialization '''e'''<sub>''p''</sub> of ''E'', then it is possible to define a global connection form in terms of the patching data between the local connection forms on the overlap regions.  In detail, a '''connection form''' on ''M'' is a system of matrices ''ω''('''e'''<sub>''p''</sub>) of 1-forms defined on each ''U''<sub>''p''</sub> that satisfy the following compatibility condition
:<math>\omega(\mathbf e_q) = (\mathbf e_p^{-1}\mathbf e_q)^{-1}d(\mathbf e_p^{-1}\mathbf e_q)+(\mathbf e_p^{-1}\mathbf e_q)^{-1}\omega(\mathbf e_p)(\mathbf e_p^{-1}\mathbf e_q).</math>
This ''compatibility condition'' ensures in particular that the exterior connection of a section of ''E'', when regarded abstractly as a section of ''E'' ⊗ Ω<sup>1</sup>''M'', does not depend on the choice of basis section used to define the connection.