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milnor's hypothesis

Proceedings of the Edinburgh Mathematical Society (1)

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On a question of Milnor concerning singularities of maps
Elmer G. Rees
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 43 / Issue 1 / February 2000

Published online by Cambridge University Press:

20 January 2009, pp. 149-153
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Restrictions are given on the dimensions m and k for which there is a map f: ℝ m → ℝk whose Jacobian has rank k in a neighbourhood of a singular point if f is either quadratic or even. The restrictions are shown to be best possible in the quadratic case.