, Volume 60, Issue 3, pp 257-280

Local analytic invariants and splitting theorems in differential analysis

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Abstract

We show that several classical problems concerning the splitting of exact sequences of spaces of differentiable functions can be reduced to questions of semicontinuity of discrete local invariants in analytic geometry. We thus provide a uniform approach to the continuous linear solution of the division, composition and extension problems in differential analysis, recovering the classical theorems and giving many new results.