2 problems

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Manturov's freeness conjecture for the virtual braid group action on the free virtual quandle
Let $FVQ_n$ be the free virtual quandle on generators $x_1,x_2,\ldots,x_n$ , and let $VB_n$ be the virtual braid group acting on $FVQ_n^{\times n}$ by the virtual quandle action. Ma…
Conjectureopengroup-actions quandles virtual-braid-groupsarXiv posted 2 days ago
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Polyak's injectivity conjecture for the pure virtual braid Lie algebra map
Polyak's injectivity conjecture. The algebra homomorphism $\psi_n$ is injective.
Conjectureopenpure-braid-groups quadratic-algebras virtual-braid-groupsarXiv posted 2 days ago

Manturov's freeness conjecture for the virtual braid group action on the free virtual quandle