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Quantum Topology


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Volume 7, Issue 1, 2016, pp. 185–201
DOI: 10.4171/QT/75

Published online: 2016-02-08

Complexity classes as mathematical axioms II

Shawn X. Cui[1], Michael H. Freedman[2] and Zhenghan Wang[3]

(1) University of California, Santa Barbara, United States
(2) University of California, Santa Barbara, USA
(3) University of California, Santa Barbara, USA

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 simplications 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 of operations are unable to effect even linear simplications of the diagrams.

Keywords: Complexity class, Link diagram, Jones polynomial

Cui Shawn, Freedman Michael, Wang Zhenghan: Complexity classes as mathematical axioms II. Quantum Topol. 7 (2016), 185-201. doi: 10.4171/QT/75