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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Essential dimension lowering mappings having dense deficiency set


Author: Mladen Bestvina
Journal: Trans. Amer. Math. Soc. 287 (1985), 787-798
MSC: Primary 54C10; Secondary 55Q99
MathSciNet review: 768741
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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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0768741-0
PII: S 0002-9947(1985)0768741-0
Keywords: One-to-one over the image of a dense set, monotone map, essential map, stable values
Article copyright: © Copyright 1985 American Mathematical Society