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On global invertibility of semi-algebraic local diffeomorphisms. (English) Zbl 1484.14112

The authors use examples to show that regularity conditions at infinity, the integral condition, locally trivial fibrations and the topological conditions are not invariant by conjugation with linear automorphisms. They also prove that the spectral conditions are invariant by conjugation with linear automorphisms, which is useful in the proofs of global injectivity. In addition, the authors relate the simple connectedness with the notion of locally trivial fibrations and gave an equivalent statement of the Jacobian conjecture by using fibrations.
Reviewer: Yan Dan (Changsha)

MSC:

14R15 Jacobian problem
14D05 Structure of families (Picard-Lefschetz, monodromy, etc.)
58K15 Topological properties of mappings on manifolds

References:

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