Complexity Classes as Mathematical Axioms II
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 May 2013
 DOI:
 10.48550/arXiv.1305.6076
 arXiv:
 arXiv:1305.6076
 Bibcode:
 2013arXiv1305.6076C
 Keywords:

 Computer Science  Computational Complexity;
 Mathematics  Geometric Topology;
 57M25;
 68Q15;
 81P68
 EPrint:
 To appear in Quantum Topology