We study mapping class groups of infinite type surfaces with isolated punctures and their actions on the $loop$ $graphs$ introduced by Bavard and Walker. We classify all of the mapping classes in these actions which are loxodromic with a WWPD action on the corresponding loop graph. The WWPD property is a weakening of Bestvina and Fujiwara’s weak proper discontinuity and is useful for constructing non-trivial quasimorphisms. We use this classification to give a sufficient criterion for subgroups of big mapping class groups to have infinite-dimensional second bounded cohomology and use this criterion to give simple proofs that certain natural subgroups of big mapping class groups have infinite dimensional second bounded cohomology.

中文翻译：

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大映射类组的 WWPD 元素

我们研究了在 Bavard 和 Walker 引入的 $loop$$graphs$ 上映射具有孤立穿孔的无限类型表面的类组及其动作。我们对这些动作中的所有映射类进行分类，这些动作在相应的循环图上具有 WWPD 动作。WWPD 性质是 Bestvina 和 Fujiwara 弱固有不连续性的弱化，可用于构造非平凡拟态。我们用这个分类给出了大映射类群的子群具有无限维第二有界上同调的充分标准，并用这个标准给出了大映射类群的某些自然子群具有无限维第二有界上同调的简单证明。