  The second author previously discussed how classical complexity separation
conjectures, we call them "axioms", have implications in three manifold
topology: polynomial length stings of operations which preserve certain Jones
polynomial evaluations cannot produce exponential simplifications of link
diagrams. In this paper, we continue this theme, exploring now more subtle
separation axioms for quantum complexity classes. Surprisingly, we now find
that similar strings are unable to effect even linear simplifications of the
diagrams.
