发表机构
Vanderbilt University; CUNY Hunter College; University of Notre Dame; Swarthmore College; Heriot-Watt University（范德堡大学; 纽约市立学院亨特学院; 圣母大学; 斯沃斯莫尔学院; 赫瑞-瓦特大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过新组合定理证明由LR曲面群等PGF子群扩张得到的图丛具有双曲性，进而表明相应曲面丛基本群为分层双曲。
AI 中文摘要
我们通过证明由第三作者和Reid构造的曲面群扩张（LR曲面群）是分层双曲的，给出了许多以曲面为纤维、以曲面为底空间且其基本群是分层双曲的曲面丛的例子。这一结果得益于一个新的关于以双曲图为底空间的双曲图丛的组合定理。该定理与先前关于图丛的组合定理不同之处在于，它适用于纤维并非适当嵌入的丛。我们应用该组合定理来建立某些图丛的双曲性，这些图丛自然产生于映射类群的抛物几何有限（PGF）子群的扩张。这些子群包括LR曲面群、有限生成的Veech群、多重扭转群的自由积，以及由Udall定理创造的许多其他例子。当PGF群具有循环外围时，我们的图丛的双曲性是证明扩张群为分层双曲的关键里程碑。
英文摘要
We give many examples of surface bundles over surfaces whose fundamental groups are hierarchically hyperbolic by showing that extensions of surface groups constructed by the third author and Reid (LR surface groups) are hierarchically hyperbolic. This is facilitated by a new combination theorem for bundles of hyperbolic graphs over a hyperbolic base. This result differs from previous combination theorems for graph bundles by being applicable to bundles where the fibers are not properly embedded. We apply our combination theorem to establish the hyperbolicity of certain graph bundles that arise naturally from extensions of parabolically geometrically finite (PGF) subgroups of mapping class groups. These subgroups include LR surface groups, finitely generated Veech groups, free products of multi-twist groups, and many other examples created by a theorem of Udall. When the PGF groups have cyclic peripherals, hyperbolicity of our graph bundle is the key milestone towards showing that the extension groups are hierarchically hyperbolic.
Comments40 pages, 4 figures, no AI
