On a canonical lift of Artin's representation to loop braid groups
نویسندگان
چکیده
منابع مشابه
On the representation theory of braid groups
This work presents an approach towards the representation theory of the braid groups Bn. We focus on finite-dimensional representations over the field of Laurent series which can be obtained from representations of infinitesimal braids, with the help of Drinfeld associators. We set a dictionary between representation-theoretic properties of these two structures, and tools to describe the repres...
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The purpose of this article is to describe a connection between the single loop space of the 2-sphere, Artin’s braid groups, a choice of simplicial group whose homotopy groups are given by modules called Lie(n), as well as work of Milnor [17, 18], and Habegger-Lin [11, 15] on “homotopy string links”. The novelty of the current article is a description of connections between these topics. 1. A t...
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To understand what a braid group is, it is easiest to visualize a braid. Consider n strands, all parallel. Consider taking the ith strand and crossing it over the very next strand. This is a braid. In fact, a braid is any sequence of crossings of the bands, provided none of the bands are self-crossing. For instance, a loop, or a band which forms a loop in the middle are not braids. Now, in orde...
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The Lawrence representation Ln,m is a family of homological representation of the braid group Bn, which specializes to the reduced Burau and the Lawrence-Krammer representation when m is 1 and 2. In this article we show that the Lawrence representation is faithful for m ≥ 2.
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The purpose of this article is to give an exposition of certain connections between the braid groups [1, 3] and classical homotopy groups which arises in joint work of Jon Berrick, Yan-Loi Wong and the authors [8, 2, 32]. These connections emerge through several other natural contexts such as Lie algebras attached to the descending central series of pure braid groups arising as Vassiliev invari...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2021
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2021.106760