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Iterated Integrals and Higher Order Invariants

Published online by Cambridge University Press:  20 November 2018

Anton Deitmar  and
Ivan Horozov
Anton Deitmar
Affiliation:
Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany, e-mail: deitmar@uni-tuebingen.de, ivan.horozov@uni-tuebingen.de
Ivan Horozov
Affiliation:
Mathematisches Institut, Auf der Morgenstelle 10, 72076 Tübingen, Germany, e-mail: deitmar@uni-tuebingen.de, ivan.horozov@uni-tuebingen.de
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Abstract

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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, higher order invariants form a free module of the algebra of full invariants.

Keywords

14F3511F1255D3558A10higher order formsiterated integrals
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 65 , Issue 3 , 01 June 2013 , pp. 544 - 552
Copyright
Copyright © Canadian Mathematical Society 2013

References

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