REVIEW 3 cited by
A new way to prove configuration reducibility using gauge theory
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We show how ideas coming out of gauge theory can be used to prove configurations in the list of ``633 unavoidable configurations" are reducible. In this paper, we prove the smallest nontrivial example, the Birkhoff diamond, is reducible using our filtered $3$- and $4$-color homology. This is a new proof of a 111-year-old result that is a direct consequence of a special (2+1)-dimensional topological quantum field theory. As part of the proof, we introduce the idea of a state-reducible configuration. Because state-reducibility does not involve Kempe switches, this leads to an independent way to verify the proof of the four color theorem. We conjecture that these gauge theoretic ideas could also lead to a non-computer-based proof of it.
Forward citations
Cited by 3 Pith papers
-
A counterexample for the polar conjecture of Spencer-Brown
A plane graph with a non-polar pentagonal face makes Spencer-Brown's parity pass return to its initial coloring after 60 steps, disproving his Polar Conjecture.
-
New relations for the vertex polynomial
The vertex polynomial satisfies local relations for digon, triangle, quadrilateral, and pentagon faces, extending it to arbitrary-degree graphs.
-
Lectures on SL(3) foams and link homology
This is an expository review of SL(3) foam evaluation and its use in categorifying the Kuperberg quantum invariant, with no new theorems.
Discussion (0). Sign in to comment.