The Gassner representation for string links
P. Kirk, C. Livingston, Z. Wang
Abstract
The Gassner representation of the pure braid group to GLn(Z[Zn]) can be extended to give a representation of the concordance group of n-strand string links to GLn(F), where F is the field of quotients of [n], F = Q(t1,...,tn); this was first observed by Le Dimet. Here we present simple new perspectives on its definition, its computation, and its applications to obtain both general results and interesting family of examples.
Create a lesson
Related papers
Combinatorial Goussarov-Polyak-Viro Formulas for the Linking Number and Low Degree Coefficients of the Conway Polynomial
Nancy Scherich, Nathaniel Song
The flip symmetry on Khovanov-Rozansky homology
Hongjian Yang
Families of knots that cannot be made Legendrian parametrically
Javier Martínez-Aguinaga
Branched real projective structures on surfaces and geometrisation of representations
Gianluca Faraco, Nicholas Rungi
Generating the twist subgroup of the level 2 mapping class group of a non-orientable closed surface
Ryoma Kobayashi
H-cobordisms, infinite cyclic covers, and real Seiberg--Witten theory
Sungkyung Kang, JungHwan Park, Masaki Taniguchi