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Iterated Integrals and Higher Order Invariants
  Published:2012-06-26
 Printed: Jun 2013
Canadian Journal of Mathematics
  • Anton Deitmar,
    Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany
  • Ivan Horozov,
    Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany
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Abstract

We show that higher order invariants of smooth functions can be written as linear combinations of full invariants times iterated integrals. The non-uniqueness of such a presentation is captured in the kernel of the ensuing map from the tensor product. This kernel is computed explicitly. As a consequence, it turns out that higher order invariants are a free module of the algebra of full invariants.
Keywords: higher order forms, iterated integrals higher order forms, iterated integrals
MSC Classifications: 14F35, 11F12, 55D35, 58A10 show english descriptions Homotopy theory; fundamental groups [See also 14H30]
Automorphic forms, one variable
unknown classification 55D35
Differential forms 14F35 - Homotopy theory; fundamental groups [See also 14H30]
11F12 - Automorphic forms, one variable
55D35 - unknown classification 55D35
58A10 - Differential forms
 
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