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A remark on first nonlinear Spencer sequence

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*E. Abadoglu*

**E-mail:** abadogle@boun.edu.tr
**Abstract.** We describe an algorithm which allows one to compute
the local formulas for first and second operators in the nonlinear first
Spencer sequence up to any order. We then indicate how to construct the
dual sequence which is related to the original sequence by a commutative
diagram where the vertical arrows are induced by the inversion in the jet
group. We hope that our approach will uncover the elementary nature of
this sequence which has recently shown to be relevant in physics and also
has some remarkable relations to connections and make it accessible to
a larger audience.

**AMSclassification.** 58A20

**Keywords.** Jets, Spencer Sequence