3 problems

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Weak homotopy type conjecture for spaces of nondegenerate spherical curves in dimension three
Dimension-three weak homotopy type conjecture. The following are weak homotopy equivalences:
Conjectureopenhomotopy-theory spherical-curvesarXiv posted 3 days ago
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Noncentral component conjecture for nondegenerate spherical curves
Noncentral component conjecture. If
Conjectureopenhomotopy-theory loop-spaces spherical-curvesarXiv posted 3 days ago
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Multiplicity monotonicity for words in the Bruhat poset
Multiplicity monotonicity conjecture. If $\sigma \in S_{n+1}$ , $w \in {\mathbf W}_n$ and $w \preceq (\sigma)$ then
Conjectureopencombinatorics spherical-curvesarXiv posted 3 days ago

Weak homotopy type conjecture for spaces of nondegenerate spherical curves in dimension three