The Index-Invariant completeness conjecture for routes to chaos

A route to chaos is a sequence of dynamical systems connected by an isotopy, and its Index-Invariant is the invariant introduced in the paper for such a route. Index-Invariant completeness conjecture. The Index-Invariant is a complete set of invariants for a route to chaos. This conjecture is motivated by Frobenius reciprocity and by the fact that the Index-Invariant is constructed using the Burau representation; the paper relates its resolution to understanding the kernel of that representation. No proof or disproof is given.