A homological representation formula of colored Alexander invariants (Q904012)

The author provides a new formulation for the colored Alexander invariant for knots, which, although depending on particular closed braid representations of the knots, can be considered as a generalization of the Burau representation formula of the Alexander polynomial. The author proves that the colored Alexander invariant can be written as a sum of traces of homological representations, called Lawrence's representations, and that truncated Lawrence's representations can be identified with a quantum \(sl_2\) braid group representations.