论文标题
相对同质组和多项式图的曲线纤维
Relative homotopy groups and Serre fibrations for polynomial maps
论文作者
论文摘要
让$ f $是$ \ Mathbb r^m $到$ \ Mathbb r^n $的多项式地图，$ m> n> 0 $，$ t_0 $是$ f $的常规值。对于一个以$ t_0 $为中心的小开机球$ d_ {t_0} $，我们表明地图$ f：f：f^{ - 1}（d_ {t_0}）\ to d_ {t_0} $是串行纤维，仅当$ f $是一个serre纤维而不是一定的简单的$ f $ sys pean $ t_ t_的$ f $时，且仅当$ f $是一个$ f $的情况下。我们通过针对这些ARC定义的相对同型组来表征纤维化$ f：f^{ - 1}（d_ {t_0}）\ d_ {t_0} $，并使用它来证明其断言。
Let $f$ be a polynomial map from $\mathbb R^m$ to $\mathbb R^n$ with $m>n>0$ and $t_0$ be a regular value of $f$. For a small open ball $D_{t_0}$ centered at $t_0$, we show that the map $f:f^{-1}(D_{t_0})\to D_{t_0}$ is a Serre fibration if and only if $f$ is a Serre fibration over a finite number of certain simple arcs starting at $t_0$. We characterize the fibration $f:f^{-1}(D_{t_0})\to D_{t_0}$ by relative homotopy groups defined for these arcs and use it to prove the assertion.
