A homological representation formula of colored Alexander invariants
Tetsuya Ito
TL;DR
This paper presents a new homological formula for colored Alexander invariants using truncated Lawrence's representation, extending the classical Burau representation approach for the Alexander polynomial.
Contribution
It introduces a homological representation formula for colored Alexander invariants, generalizing the Burau representation method.
Findings
Derived a homological formula for colored Alexander invariants
Connected the formula to truncated Lawrence's representation
Generalized the classical Burau representation approach
Abstract
We give a formula of the colored Alexander invariant in terms of the homological representation of the braid groups which we call truncated Lawrence's representation. This formula generalizes the famous Burau representation formula of the Alexander polynomial.
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