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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Iterated integrals, fundamental groups and covering spaces
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by Kuo Tsai Chen PDF
Trans. Amer. Math. Soc. 206 (1975), 83-98 Request permission

Abstract:

Differential $1$-forms are integrated iteratedly along paths in a differentiable manifold $X$. The purpose of this article is to consider those iterated integrals whose value along each path depends only on the homotopy class of the path. The totality of such integrals is shown to be dual, in an appropriate sense, to the “maximal” residually torsion free nilpotent quotient of the fundamental group ${\pi _1}(X)$. Taken as functions on the universal covering space $\tilde X$, these integrals separate points of $\tilde X$ if and only if ${\pi _1}(X)$ is residually torsion free nilpotent.
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Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 206 (1975), 83-98
  • MSC: Primary 58A10
  • DOI: https://doi.org/10.1090/S0002-9947-1975-0377960-0
  • MathSciNet review: 0377960