On the Geometry of Some Braid Group Representations

Risultato della ricerca: Contributo in libroChapter

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.
Lingua originaleEnglish
Titolo della pubblicazione ospiteKnots, Low-Dimensional Topology and Applications
EditorCC Adams, CMcA Gordon, V Jones, LH Kauffman, S Lambropoulou, KC Millett, J Przytycki, RL Ricca, R Sazdanovic
Pagine287-308
Numero di pagine22
Volume2019
Stato di pubblicazionePubblicato - 2019

Keywords

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

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