Synthetic differential geometry of Chen's iterated integrals

DOI10.13164/MA.2014.10zbMATH Open1338.51015arXiv1406.0075OpenAlexW2963978884WikidataQ115238882 ScholiaQ115238882MaRDI QIDQ3463789

Hirokazu Nishimura

Publication date: 20 January 2016

Published in: Mathematics for Application (Search for Journal in Brave)

Abstract: Chen's iterated integrals are treated within synthetic differential geometry. The main result is that iterated integrals produce a subcomplex of the de Rham complex on the free path space as well as based path spaces.

Full work available at URL: https://arxiv.org/abs/1406.0075

zbMATH Keywords

de Rham complexpath spacesynthetic differential geometrybar complexHochschild complexChen's iterated integrals

Mathematics Subject Classification ID

Category-theoretic methods and results in associative algebras (except as in 16D90) (16B50) Differential forms in global analysis (58A10) de Rham cohomology and algebraic geometry (14F40) Synthetic differential geometry (51K10)

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