Advanced Studies in Pure Mathematics

Hyperplane arrangements, local system homology and iterated integrals

Toshitake Kohno

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Abstract

We review some aspects of the homology of a local system on the complement of a hyperplane arrangement. We describe a relationship between linear representations of the braid groups due to R. Lawrence, D. Krammer and S. Bigelow and the holonomy representations of the KZ connection. We explain a method to describe such representations by the iterated integrals of logarithmic 1-forms.

Article information

Source
Arrangements of Hyperplanes — Sapporo 2009, H. Terao and S. Yuzvinsky, eds. (Tokyo: Mathematical Society of Japan, 2012), 157-174

Dates
Received: 16 June 2010
Revised: 14 January 2011
First available in Project Euclid: 24 November 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1543085008

Digital Object Identifier
doi:10.2969/aspm/06210157

Mathematical Reviews number (MathSciNet)
MR2933796

Zentralblatt MATH identifier
1261.20037

Subjects
Primary: 20F36: Braid groups; Artin groups 52C35: Arrangements of points, flats, hyperplanes [See also 32S22] 33C60: Hypergeometric integrals and functions defined by them ($E$, $G$, $H$ and $I$ functions)

Keywords
Hyperplane arrangement Salvetti complex local system KZ connection conformal field theory braid group configuration space iterated integral

Citation

Kohno, Toshitake. Hyperplane arrangements, local system homology and iterated integrals. Arrangements of Hyperplanes — Sapporo 2009, 157--174, Mathematical Society of Japan, Tokyo, Japan, 2012. doi:10.2969/aspm/06210157. https://projecteuclid.org/euclid.aspm/1543085008


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