剪刀自同构群II：Solomon-Tits定理
Scissors automorphism groups II: Solomon-Tits theorems
AI总结：
本文证明了在欧几里得、双曲或球面几何中，由点或超平面生成的测地子空间集合的正则非平凡子空间的poset的实现在球面 wedge 中等价，为后续计算剪刀自同构群的同调奠定基础。
摘要：
Solomon-Tits定理指出，有限维向量空间的正则非平凡子空间的poset的实现在球面wedge中等价。本文证明了在欧几里得、双曲或球面几何中，由点或超平面生成的测地子空间集合的正则非平凡子空间的poset的实现在球面wedge中等价，为后续计算剪刀自同构群的同调奠定基础。
英文摘要：
The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we prove a variant of this result for collections of geodesic subspaces of Euclidean, hyperbolic, or spherical geometry, assuming the collection is generated either by points or by hyperplanes. In the third paper of this series of papers, we will combine this with the homological stability theorems from the first paper to compute the homology of groups of scissors automorphisms in these geometries.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
