A research of open book decomposition of 3-manifolds

很明显，开卷分解的Alexander多项式（相当于Conway多项式）在估计开卷分解的复杂性方面起着有效的作用，这是我们在之前的研究中定义的。从这个观察中，我们得到了一个预测，即打开书分解的纤维表面的映射类群的Johnson-Morita表示将有助于构造一个新的打开书分解的不变量，该不变量给我们比Alexander多项式更严格的复杂性估计。

It has become clear that the Alexander polynomial (equivalently the Conway polynomial) of open book decompositions plays an effective role for an estimation of the complexity of open book decompositions, which we defined in our previous research. From this observation, we have obtained a prediction that the Johnson-Morita representation of the mapping class group of the fiber surface of an open book decomposition will be useful to constract a new invariant of open book decomposition which gives us stricter estimation of the complexity than the Alexander polynomial.