Given a compact complex manifold X and a integrable Beltrami differential $\varphi \in A^{0,1}(X,T_X^{1,0})$, we introduce a double complex structure on $A^{•,•}(X)$ naturally determined by ϕ and study its Bott-Chern cohomology. In particular, we establish a deformation theory for Bott-Chern cohomology and use it to compute the deformed Bott-Chern cohomology for the Iwasawa manifold and the holomorphically parallelizable Nakamura manifold. The $\partial {\overline{\partial }}_{\varphi }$-lemma is studied and we show a compact complex manifold satisfying $\partial {\overline{\partial }}_{\varphi }$-lemma is formal.

中文翻译：

---

关于变形的Bott-Chern同调

给定一个紧凑的复流形X和一个可积的Beltrami微分$\varphi \in {\mathrm{一种}}^{0，\mathrm{1个}}（X，{Ť}_X^{\mathrm{1个}，0}）$，我们在上引入了双重复杂结构 ${\mathrm{一种}}^{•，•}（X）$自然地确定φ，并研究其博特-陈省身上同调。特别地，我们建立了Bott-Chern同调的变形理论，并用它来计算Iwasawa流形和全纯可并行化Nakamura流形的Bott-Chern形变。这$\partial {\overline{\partial }}_{\varphi }$研究了-引理，并证明了满足 $\partial {\overline{\partial }}_{\varphi }$-引理是正式的。