Higher holonomy maps for hyperplane arrangements

Abstract

We develop a method to construct representations of the homotopy 2-groupoid of a manifold as a 2-category by means of Chen’s formal homology connections. As an application we describe 2-holonomy maps for hyperplane arrangements and discuss representations of the category of braid cobordisms.

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Correspondence to Toshitake Kohno.

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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.

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Kohno, T. Higher holonomy maps for hyperplane arrangements. European Journal of Mathematics 6, 905–927 (2020). https://doi.org/10.1007/s40879-019-00382-z

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Keywords

  • Braid group
  • Iterated integral
  • Formal homology connection
  • Hyperplane arrangement
  • Higher holonomy
  • 2-Category
  • Braid cobordism

Mathematics Subject Classification

  • 20F36
  • 57M25
  • 55P62