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- W4292950696 abstract "Let $f$ be a polynomial map from $mathbb R^m$ to $mathbb R^n$ with $m>n$. Fix a point $t_0in mathbb R^n$ and choose an $n$-dimensional ball $D_{t_0}$ centered at $t_0$ and small enough with respect to the canonical stratification of $mathbb R^n$ given according to the bifurcation set of $f$. We show that the restriction of $f$ to $f^{-1}(D_{t_0})$ is a Serre fibration if and only if certain relative homotopy groups defined for arcs on the closures of strata on $D_{t_0}$ with endpoint $t_0$ are all trivial. We present an example of atypical fiber of a fibration over an arc that cannot be detected by the integral homology groups of the atypical fiber and its nearby fiber, but is detected by our relative homotopy groups." @default.
- W4292950696 created "2022-08-24" @default.
- W4292950696 creator A5024434349 @default.
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- W4292950696 date "2022-08-22" @default.
- W4292950696 modified "2023-09-27" @default.
- W4292950696 title "Relative homotopy groups and Serre fibrations for polynomial maps" @default.
- W4292950696 doi "https://doi.org/10.48550/arxiv.2208.10055" @default.
- W4292950696 hasPublicationYear "2022" @default.
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