Formal connections, higher holonomy functors and iterated integrals

Toshitake Kohno

doi:10.1016/j.topol.2021.107985

Formal connections, higher holonomy functors and iterated integrals

Toshitake Kohno

School of Interdisciplinary Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

This is a review on representations of the path n-groupoid of a manifold as an n-category based on iterated integrals developed by K.-T. Chen. We describe higher holonomy functors for the path n-groupoid and the homotopy n-groupoid using the notion of formal connections.

Original language	English
Article number	107985
Journal	Topology and its Applications
DOIs	https://doi.org/10.1016/j.topol.2021.107985
Publication status	Accepted/In press - 2022

Keywords

2-connection
Formal connection
Higher holonomy
Iterated integral
n-category
Path groupoid

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10.1016/j.topol.2021.107985

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title = "Formal connections, higher holonomy functors and iterated integrals",

abstract = "This is a review on representations of the path n-groupoid of a manifold as an n-category based on iterated integrals developed by K.-T. Chen. We describe higher holonomy functors for the path n-groupoid and the homotopy n-groupoid using the notion of formal connections.",

keywords = "2-connection, Formal connection, Higher holonomy, Iterated integral, n-category, Path groupoid",

author = "Toshitake Kohno",

note = "Funding Information: The author is partially supported by Grant-in-Aid for Scientific Research, KAKENHI 16H03931 , Japan Society of Promotion of Science and by World Premier Research Center Initiative , MEXT , Japan. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",

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language = "English",

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N2 - This is a review on representations of the path n-groupoid of a manifold as an n-category based on iterated integrals developed by K.-T. Chen. We describe higher holonomy functors for the path n-groupoid and the homotopy n-groupoid using the notion of formal connections.

AB - This is a review on representations of the path n-groupoid of a manifold as an n-category based on iterated integrals developed by K.-T. Chen. We describe higher holonomy functors for the path n-groupoid and the homotopy n-groupoid using the notion of formal connections.

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KW - Formal connection

KW - Higher holonomy

KW - Iterated integral

KW - n-category

KW - Path groupoid

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DO - 10.1016/j.topol.2021.107985

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JO - Topology and its Applications

JF - Topology and its Applications

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ER -

Formal connections, higher holonomy functors and iterated integrals

Abstract

Keywords

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