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The Hurwitz Equivalence Problem is Undecidable

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arxiv math/0511153 v2 pith:OUE4MOTZ submitted 2005-11-07 math.LO math.AG

E. Liberman , M. Teicher This is my paper · ORCID
classification math.LOmath.AG
keywords equivalencehurwitzproblemundecidablefactorizationsbraidconsequencedelta
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abstract

In this paper, we prove that the Hurwitz equivalence problem for 1-factorizations in $F_2 \oplus F_2$ is undecidable, and as a consequence, the Hurwitz equivalence problem for $\Delta^2$-factorizations in the braid groups $B_n, n\geq 5$ is also undecidable.

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  1. Crossing matrix and a polynomial invariant of braid systems up to Hurwitz equivalence

    math.GT 2026-01 conditional novelty 3.0 of 10

    The product of characteristic polynomials of crossing matrices of the components of a braid system is invariant under Hurwitz equivalence, and its essential eigenvalues detect Euler fusion/fission.

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