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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.

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Authors and Affiliations

  1. Department of Mathematics, University of Toronto, M 5S 1A1, Toronto, Canada

    Edward Bierstone & Pierre D. Milman

Authors
  1. Edward Bierstone
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  2. Pierre D. Milman
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Additional information

Dedicated to the memory of David P. Milman

Research partially supported by NSERC operating grant A9070.

Supported by NSERC University Research Fellowship and operating grant A8849.

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Bierstone, E., Milman, P.D. Local analytic invariants and splitting theorems in differential analysis. Israel J. Math. 60, 257–280 (1987). https://doi.org/10.1007/BF02780394

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  • DOI: https://doi.org/10.1007/BF02780394

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