Geodesic
Low-Dimensional Pure Braid Group Representations Via Nilpotent Flat Connections
Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 643-672

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In this note we discuss low-dimensional matrix representations of pure braid group (on three and four strands) obtained via holonomy of suitable nilpotent flat connections. Flatness is directly enforced by means of the Arnol'd relations. These explicit representations are used to investigate Brunnian and “nested” Brunnian phenomena. 
@article{BUMI_2013_9_6_3_a8,
     author = {Benvegn\`u, Alberto and Spera, Mauro},
     title = {Low-Dimensional {Pure} {Braid} {Group} {Representations} {Via} {Nilpotent} {Flat} {Connections}},
     journal = {Bollettino della Unione matematica italiana},
     pages = {643--672},
     publisher = {mathdoc},
     volume = {Ser. 9, 6},
     number = {3},
     year = {2013},
     mrnumber = {3202844},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a8/}
}
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Benvegnù, Alberto; Spera, Mauro. Low-Dimensional Pure Braid Group Representations Via Nilpotent Flat Connections. Bollettino della Unione matematica italiana, Série 9, Tome 6 (2013) no. 3, pp. 643-672. http://geodesic.mathdoc.fr/item/BUMI_2013_9_6_3_a8/