论文标题
在不可定向的3个杂志的开放书籍上
On open books for nonorientable 3-manifolds
论文作者
论文摘要
我们表明，克拉森属的单曲子是$ p^2 \ times s^1 $的两本开放书，是lickorish的$ y $ - 瘤形成，也称为crosscap幻灯片。同样，我们表明$ s^2 \ widetilde {\ times} s^1 $允许一本属属，其单片是crosscap transiposition。此外，我们表明$ p^2 \ times s^1 $和$ s^2 \ widetilde {\ times} s^1 $无限地允许许多同构属书籍，其单层是共同非异型的。此外，我们还包括一个简单的观察，以$ p^2 \ times s^1 $和$ s^2 \ widetilde {\ times} s^1 $的稳定等价类别的稳定等价类别。最后，我们制定了Gabai定理的版本，涉及穆拉苏吉（Murasugi）的开放书籍总和，而没有在页面上实现任何可正度性假设。
We show that the monodromy of Klassen's genus two open book for $P^2 \times S^1$ is the $Y$-homeomorphism of Lickorish, which is also known as the crosscap slide. Similarly, we show that $S^2 \widetilde{\times} S^1$ admits a genus two open book whose monodromy is the crosscap transposition. Moreover, we show that each of $P^2 \times S^1$ and $S^2 \widetilde{\times} S^1$ admits infinitely many isomorphic genus two open books whose monodromies are mutually nonisotopic. Furthermore, we include a simple observation about the stable equivalence classes of open books for $P^2 \times S^1$ and $S^2 \widetilde{\times} S^1$. Finally, we formulate a version of Gabai's theorem about the Murasugi sum of open books, without imposing any orientability assumption on the pages.
