  We define the principal divisor of a free noncommuatative function. We use
these divisors to compare the determinantal singularity sets of free
noncommutative functions. We show that the divisor of a noncommutative rational
function is the difference of two polynomial divisors.
  We formulate a nontrivial theory of cohomology, fundamental groups and
covering spaces for tracial free functions. We show that the natural
fundamental group arising from analytic continuation for tracial free functions
is a direct sum of copies of $\mathbb{Q}$. Our results contrast the classical
case, where the analogous groups may not be abelian, and the free case, where
free universal monodromy implies such notions would be trivial.
