Bott–Chern cohomology of solvmanifolds
Bott–Chern cohomology of solvmanifolds
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DOI：
10.1007/s10455-017-9560-6
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发表时间：
2012-12
影响因子：
0.7
通讯作者：
Daniele Angella;H. Kasuya
中科院分区：
文献类型：
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作者：
Daniele Angella;H. Kasuya
研究了向量空间二重复的子复允许计算bot - chern上同调的条件。本文主要研究了一类特殊的可并行化复溶剂流形和分裂型溶剂流形的bot - chern上同调。更精确地说，我们可以构造明确的有限维双复复来计算复李群的紧商的bot - chen上同调。作为应用，我们计算了复可并行Nakamura流形与完全可解Nakamura流形的bot - chen上同调。特别是后者证明了在复杂结构的变形下满足引理的性质不是强封闭的。
We study conditions under which sub-complexes of a double complex of vector spaces allow to compute the Bott–Chern cohomology. We are especially aimed at studying the Bott–Chern cohomology of special classes of solvmanifolds, namely, complex parallelizable solvmanifolds and solvmanifolds of splitting type. More precisely, we can construct explicit finite-dimensional double complexes that allow to compute the Bott–Chern cohomology of compact quotients of complex Lie groups, respectively, of some Lie groups of the typewhereNis nilpotent. As an application, we compute the Bott–Chern cohomology of the complex parallelizable Nakamura manifold and of the completely solvable Nakamura manifold. In particular, the latter shows that the property of satisfying the-Lemma is not strongly closed under deformations of the complex structure.