A generalized Burau representation for string links
نویسندگان
چکیده
منابع مشابه
A Generalized Burau Representation for String Links
A 2-variable matrix B ∈ GLn(Z[u±1, v±1]) is defined for any n-string link, generalizing the Burau matrix of an nbraid. The specialization u = 1, v = t−1 recovers the generalized Burau matrix recently defined by X. S. Lin, F. Tian and Z. Wang using probabilistic methods. The specialization u = t−1, v = 1 results in a matrix with a natural algebraic interpretation, and one that yields homological...
متن کاملVersion: 2/99 A GENERALIZED BURAU REPRESENTATION FOR STRING LINKS
ABSTRACT. A 2-variable matrix B ∈ GLn(Z[u±1, v±1]) is defined for any n-string link, generalizing the Burau matrix of an n-braid. The specialization u = 1, v = t−1 recovers the generalized Burau matrix recently defined by X. S. Lin, F. Tian and Z. Wang using probabilistic methods. The specialization u = t−1, v = 1 results in a matrix with a natural algebraic interpretation, and one that yields ...
متن کاملBurau Representation and Random Walk on String Links
Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the trans...
متن کاملBurau Representation and Random Walks on String Links
Using a probabilistic interpretation of the Burau representation of the braid group offered by Vaughan Jones, we generalize the Burau representation to a representation of the semigroup of string links. This representation is determined by a linear system, and is dominated by finite type string link invariants. For positive string links, the representation matrix can be interpreted as the trans...
متن کاملThe Gassner Representation for String Links
The Gassner representation of the pure braid group to GLn(Z[Z ]) 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 Z[Z ], F = Q(t1, · · · , tn); this was first observed by Le Dimet. Here we give a cohomological interpretation of this extension. Our first application is to prove that the representation is h...
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ژورنال
عنوان ژورنال: Pacific Journal of Mathematics
سال: 2001
ISSN: 0030-8730
DOI: 10.2140/pjm.2001.197.241