论文标题
在一致或同型球上扭曲
Gluck twists on concordant or homotopic spheres
论文作者
论文摘要
让$ m $成为紧凑型$ 4 $ - manifold，让$ s $和$ t $嵌入$ 2 $ -spheres $ m $，都带有微不足道的普通捆绑包。我们为Gluck Twist Operation在$ s $和$ s $和$ t $的$ 4 $ manifolds和$ t $上撰写$ m_s $和$ m_t $。我们表明，如果$ s $和$ t $是一致的，则$ m_s $和$ m_t $是$ s $ -cobordant，因此，如果$π_1（m）$很好，则$ m_s $和$ m_t $是同型。同样，如果$ s $和$ t $是同型的，那么我们表明$ m_s $和$ m_t $是简单的同型。在进一步的假设下，我们推断出$ m_s $和$ m_t $是同型的。我们表明，通过举例说明$ s $和$ t $是同质的，但$ m_s $和$ m_t $不是同型的，则表明需要其他假设。我们还举一个例子，其中$ s $和$ t $是同质的，$ m_s $和$ m_t $是同型的，但不是差异。
Let $M$ be a compact $4$-manifold and let $S$ and $T$ be embedded $2$-spheres in $M$, both with trivial normal bundle. We write $M_S$ and $M_T$ for the $4$-manifolds obtained by the Gluck twist operation on $M$ along $S$ and $T$ respectively. We show that if $S$ and $T$ are concordant, then $M_S$ and $M_T$ are $s$-cobordant, and so if $π_1(M)$ is good, then $M_S$ and $M_T$ are homeomorphic. Similarly, if $S$ and $T$ are homotopic then we show that $M_S$ and $M_T$ are simple homotopy equivalent. Under some further assumptions, we deduce that $M_S$ and $M_T$ are homeomorphic. We show that additional assumptions are necessary by giving an example where $S$ and $T$ are homotopic but $M_S$ and $M_T$ are not homeomorphic. We also give an example where $S$ and $T$ are homotopic and $M_S$ and $M_T$ are homeomorphic but not diffeomorphic.
