Complexity classes as mathematical axioms II

Shawn X. Cui, Michael H. Freedman, Zhenghan Wang

Research output: Contribution to journalArticlepeer-review


The second author previously discussed how classical complexity separation conjectures, we call them “axioms,” have implications in three manifold topology: polynomial length strings 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 and that similar strings of operations are unable to The effect even linear simplifications of the diagrams.

Original languageEnglish
Pages (from-to)185-201
Number of pages17
JournalQuantum Topology
Issue number1
StatePublished - 2016
Externally publishedYes

Bibliographical note

Publisher Copyright:
© European Mathematical Society.


  • Complexity class
  • Jones polynomial
  • Link diagram

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology


Dive into the research topics of 'Complexity classes as mathematical axioms II'. Together they form a unique fingerprint.

Cite this