O-极小结构群群的上同调：无穷小子群的非循环性
Cohomology of groups in o-minimal structures: acyclicity of the infinitesimal subgroup
摘要：
通过最近对Pillay的一些性质的研究，证明了饱和o-极小结构的可定义紧群是紧李群通过一个无挠的无挠的正规可除子群（称为无穷小子群）的扩张.我们证明了无穷小子群是上同调非循环的。这意味着可定义紧群和李群之间的函子对应保持上同调。
英文摘要：
By recent work on some conjectures of Pillay, each definably compact group in a saturated o-minimal structure is an expansion of a compact Lie group by a torsion free normal divisible subgroup, called its infinitesimal subgroup. We show that the infinitesimal subgroup is cohomologically acyclic. This implies that the functorial correspondence between definably compact groups and Lie groups preserves the cohomology.
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。
