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Pure Mathematics 2025
一类泊松流形的同调
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Abstract:
本文旨在探讨一类特定的泊松流形——Iwasawa流形和幂零流形的同调群。通过引入全纯泊松流形的概念，运用Koszul-Brylinski同调和全纯Koszul-Brylinski同调的工具，我们计算了这些流形的同调群。结果表明，幂零流形在某些条件下具有可预见的同调结构，这为理解泊松几何中的深层次联系提供了新的视角。
This paper aims to explore the homology groups of a specific class of Poisson manifolds, namely Iwasawa manifolds and nilpotent manifolds. By introducing the concept of holomorphic Poisson manifolds and using tools such as Koszul-Brylinski homology and holomorphic Koszul-Brylinski homology, we compute the homology groups of these manifolds. The results show that nilpotent manifolds possess predictable homological structures under certain conditions, offering new perspectives for understanding the deep connections in Poisson geometry.
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