The Long--Moody construction and twisted Alexander invariants
Akihiro Takano
TL;DR
This paper explores the Long--Moody construction, showing its matrix representation via Fox derivation and establishing its connection with twisted Alexander invariants, advancing understanding of braid group representations.
Contribution
It demonstrates how the Long--Moody construction's matrix form can be expressed using Fox derivation and links it to twisted Alexander invariants, providing new insights.
Findings
Matrix presentation via Fox derivation established
Relation between Long--Moody construction and twisted Alexander invariants shown
Enhanced understanding of braid group representations
Abstract
In 1994, Long and Moody introduced a method to construct a new representation of the braid group from the representation of the braid group or the semidirect product of the braid group and the free group. In this paper, we show that its matrix presentation is written using the Fox derivation, and also a relation with twisted Alexander invariants.
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Taxonomy
TopicsGeometric and Algebraic Topology · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology