Free groups and finite type invariants of pure braids

1999/09/14 by Jacob Mostovoy, Mostovoy, Jacob, Simon Willerton +1
Mathematics · #FOS: Mathematics #Geometric Topology (math.GT) #math.GT

paper · pdf · doi:10.48550/arxiv.math/9909070

14 pages, many figures

arxiv created 1999/09/14 · arxiv updated 2009/11/30

Abstract

Finite type invariants (also known as Vassiliev invariants) of pure braids are considered from a group-theoretic point of view. New results include a construction of a universal invariant with integer coefficients based on the Magnus expansion of a free group and a calculation of numbers of independent invariants of each type for all pure braid groups.

Related

• Vassiliev invariants I: Braid groups and rational homotopy theory
• On braids and groups G_n^k
• On an invariant of pure braids
• The BNS-invariant for the pure braid groups
• Knot invariants from representations of braids by automorphisms of a free group