Surjectivity of linear operators and semialgebraic global diffeomorphisms
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866914774566043648 |
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| author | Braun, Francisco Dias, Luis Renato Gonçalves Santos, Jean Venato |
| author_facet | Braun, Francisco Dias, Luis Renato Gonçalves Santos, Jean Venato |
| contents | We prove that a $C^{\infty}$ semialgebraic local diffeomorphism of $\mathbb{R}^n$ with non-properness set having codimension greater than or equal to $2$ is a global diffeomorphism if $n-1$ suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of $\mathbb{R}^n$. Our conjecture implies a very known conjecture of Z. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2110_01051 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Surjectivity of linear operators and semialgebraic global diffeomorphisms Braun, Francisco Dias, Luis Renato Gonçalves Santos, Jean Venato Geometric Topology We prove that a $C^{\infty}$ semialgebraic local diffeomorphism of $\mathbb{R}^n$ with non-properness set having codimension greater than or equal to $2$ is a global diffeomorphism if $n-1$ suitable linear partial differential operators are surjective. Then we state a new analytic conjecture for a polynomial local diffeomorphism of $\mathbb{R}^n$. Our conjecture implies a very known conjecture of Z. Jelonek. We further relate the surjectivity of these operators with the fibration concept and state a general global injectivity theorem for semialgebraic mappings which turns out to unify and generalize previous results of the literature. |
| title | Surjectivity of linear operators and semialgebraic global diffeomorphisms |
| topic | Geometric Topology |
| url | https://arxiv.org/abs/2110.01051 |