On the Geometry of Some Braid Group Representations

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In this note we report on recent differential geometric constructions aimed at devising representations of braid groups in various contexts, together with some applications in different domains of mathematical physics. First, the classical Kohno construction for the 3- and 4-strand pure braid groups P_3 and P_4 is explicitly implemented by resorting to the Chen-Hain-Tavares nilpotent connections and to hyperlogarithmic calculus, yielding unipotent representations able to detect Brunnian and nested Brunnian phenomena. Physically motivated unitary representations of Riemann surface braid groups are then described, relying on Bellingeri's presentation and on the geometry of Hermitian-Einstein holomorphic vector bundles on Jacobians, via representations of Weyl-Heisenberg groups.
Original languageEnglish
Title of host publicationKnots, Low-Dimensional Topology and Applications
EditorsCC Adams, CMcA Gordon, V Jones, LH Kauffman, S Lambropoulou, KC Millett, J Przytycki, RL Ricca, R Sazdanovic
Pages287-308
Number of pages22
Volume2019
DOIs
Publication statusPublished - 2019

Keywords

  • Braid groups, Chen iterated integrals, Hermitian-Einstein bundles, Weyl-Heisenberg groups

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