Editing Noncommutative geometry (section)

===In the sense of Connes <span class="anchor" id="Connes connection"></span>===
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A '''Connes connection''' is a noncommutative generalization of a [[connection (mathematics)|connection]] in [[differential geometry]]. It was introduced by [[Alain Connes]], and was later generalized by [[Joachim Cuntz]] and [[Daniel Quillen]].

==== Definition ====
Given a right ''A''-module ''E'', a Connes connection on ''E'' is a linear map
:<math>\nabla : E \to E \otimes_A \Omega^1 A</math>
that satisfies the [[Product rule (calculus)|Leibniz rule]] <math>\nabla_r(sa) = \nabla_r(s) a + s \otimes da</math>.<ref>{{harvnb|Vale|2009|loc=Definition 8.1.}}</ref>
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