Advanced Studies in Pure Mathematics

Hyperplane arrangements, local system homology and iterated integrals

Toshitake Kohno

Full-text: Open access


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

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

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

Permanent link to this document euclid.aspm/1543085008

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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)

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


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.

Export citation