Projected and Near-Projected Embeddings

A stable smooth map f : N → M is called k-realizable if its composition with the inclusion ⊂ × ℝk C0-approximable by embeddings; and a k-prem same C∞-approximable embeddings, or, equivalently, lifts vertically to embedding ↪ ℝk. It obvious that k-prem, then it k-realizable. We refute so-called “prem conjecture” converse holds. Namely, for each n = 4k+3 ≥ 15 there exists immersion Sn ↬ ℝ2n−7 3-realizable but not 3-prem. also prove in wide range of cases. fold Nn M2n−q q ≤ 2k−3; or < n/2 k 1; ∈ {2k−1, 2k−2} {2, 4, 8} sufficiently large.