Low-dimensional pure braid group representations via nilpotent flat connections

Mauro Spera; Alberto Benvegnù

Low-dimensional pure braid group representations via nilpotent flat connections

Mauro Spera, Alberto Benvegnù

Research output: Contribution to journal › Article › peer-review

Abstract

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.

Original language	English
Pages (from-to)	643-672
Number of pages	30
Journal	BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA
Volume	VI (2013)
Publication status	Published - 2013

Keywords

Pure braid groups, higher order braid invariants, flat connections, Chen iterated integrals, hyperlogarithms

Cite this

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title = "Low-dimensional pure braid group representations via nilpotent flat connections",

abstract = "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{\textquoteright}d relations. These explicit representations are used to investigate Brunnian and “nested” Brunnian phenomena.",

keywords = "Pure braid groups, higher order braid invariants, flat connections, Chen iterated integrals, hyperlogarithms, Pure braid groups, higher order braid invariants, flat connections, Chen iterated integrals, hyperlogarithms",

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year = "2013",

language = "English",

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T1 - Low-dimensional pure braid group representations via nilpotent flat connections

AU - Spera, Mauro

AU - Benvegnù, Alberto

PY - 2013

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N2 - 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.

AB - 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.

KW - Pure braid groups, higher order braid invariants, flat connections, Chen iterated integrals, hyperlogarithms

UR - http://hdl.handle.net/10807/54856

M3 - Article

VL - VI (2013)

SP - 643

EP - 672

JO - Bolletino dell Unione Matematica Italiana

JF - Bolletino dell Unione Matematica Italiana

SN - 1972-6724

ER -

Low-dimensional pure braid group representations via nilpotent flat connections

Abstract

Keywords

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