The orbits of the up-down action of classical and virtual braid diagrams on Z^n are completely determined: trace alone for virtual braids, trace plus a parity-type count for classical braids.
The Hurwitz Equivalence Problem is Undecidable
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
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.
citation-role summary
background 1
citation-polarity summary
fields
math.GT 1years
2024 1verdicts
CONDITIONAL 1roles
background 1polarities
unclear 1representative citing papers
citing papers explorer
-
Orbits by the up-down action of braid diagrams
The orbits of the up-down action of classical and virtual braid diagrams on Z^n are completely determined: trace alone for virtual braids, trace plus a parity-type count for classical braids.