What does knot theory have to do with P^#P != NP ?

[R.A. Hettinga]

<http://ephermata.livejournal.com/190880.html?mode=reply>


David Molnar (ephermata) wrote,
@ 2008-10-04 01:59:00



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What does knot theory have to do with P^#P != NP ?
I didn't know, but Michael H. Freedman has an answer - by assuming  
that the complexity class P^#P is not equal to NP, you can prove a new  
theorem in knot theory!

Complexity Classes as Mathematical Axioms

M. Freedman
(Submitted on 30 Sep 2008)

Abstract: Treating a conjecture, P^#P != NP, on the separation of  
complexity classes as an axiom, an implication is found in three  
manifold topology with little obvious connection to complexity theory.  
This is reminiscent of Harvey Friedman's work on finitistic  
interpretations of large cardinal axioms.

http://arxiv.org/abs/0810.0033