变分算子的核与开卷周期
Kernel of the variation operator and periodicity of the open books
摘要：
我们考虑一个可平行化的$2n$ -流形$F$，它具有$n$ -球面的楔积的同伦类型，并证明了保持边界$\partial F$逐点固定并诱导平凡变分算子的保向仿射的伪合痕类群是所有同伦$(2n+1)$ -球面的群由$H_n\bigl(F; Sπ_n(SO(n))\bigr)$的中心扩张.然后我们应用这个结果来研究具有简单翻开书分解的流形的分支循环覆盖的周期性，并将Durfee、Kauffman和Stevens之前的结果扩展到7维和15维。
英文摘要：
We consider a parallelizable $2n$-manifold $F$ which has the homotopy type of the wedge product of $n$-spheres and show that the group of pseudo-isotopy classes of orientation preserving diffeomorphisms that keep the boundary $\partial F$ pointwise fixed and induce the trivial variation operator is a central extension of the group of all homotopy $(2n+1)$-spheres by $H_n\bigl(F; Sπ_n(SO(n))\bigr)$. Then we apply this result to study the periodicity properties of branched cyclic covers of manifolds with simple open book decompositions and extend the previous results of Durfee, Kauffman and Stevens to dimensions 7 and 15.
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