Essential dimension lowering mappings having dense deficiency set

Bestvina, Mladen

doi:10.1090/S0002-9947-1985-0768741-0

Essential dimension lowering mappings having dense deficiency set
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Trans. Amer. Math. Soc. 287 (1985), 787-798 Request permission

Abstract:

Two classes of surjective maps $f:{S^m} \to {S^n}$ that are one-to-one over the image of a dense set are constructed. We show that for $m,n \geq 3$ there is a monotone surjection $f:{S^m} \to {S^n}$ that is one-to-one over the image of a dense set; and for $3 \leq n \leq m \leq 2n - 3$, each element of ${\pi _m}({S^n})$ can be represented as a monotone surjection $f:{S^m} \to {S^n}$ that is one-to-one over the image of a dense set.

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