On the metastable Mabillard-Wagner conjecture

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The purpose of this note is to attract attention to the following conjecture (metastable r-fold Whitney trick) by clarifying its status as not having a complete proof, in the sense described in the paper. Assume that D=D₁ Dᵣ is disjoint union of r disks of dimension s, f:D→ Bᵈ a proper PL map such that f∂ D₁∩∩ f∂ Dᵣ=, rd≥ (r+1)s+3 and d≥ s+3. If the map fʳ:∂(D₁×× Dᵣ)→ (Bᵈ)ʳ-{(x,x,,x)∈(Bᵈ)ʳ|x∈ Bᵈ} extends to D₁×× Dᵣ, then there is a PL map f:D→ Bᵈ such that f=f Dᵣ∪∂ D fD₁∩∩ fDᵣ=.