A topological model for the coloured Alexander invariants

Abstract

Coloured Alexander polynomials form a sequence of non-semisimple quantum invariants coming from the representation theory of the quantum group Uq(sl(2)) at roots of unity. This sequence recovers the original Alexander polynomial as the first term. We give a topological model for these invariants, showing that they can be obtained as graded intersection pairings between homology classes in a covering of the configuration space in the punctured disc.