A research of open book decomposition of 3-manifolds

很明显，亚历山大多项式（相当于康威多项式）的开卷分解起着有效的作用，估计开卷分解的复杂性，我们在我们以前的研究中定义。由此，我们得到了一个预言：开书分解的纤维曲面的映射类群的Johnson-Morita表示将有助于构造一个新的开书分解不变量，它比亚历山大多项式给出了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.