Spinc structures on real Bott manifolds
Anna Gąsior, Rafał Lutowski
本文研究实Bott流形上spinc结构的存在性问题，给出了其存在的充分必要条件。
我们给出了实Bott流形上存在spinc结构的一个充分必要条件。
We give a necessary and sufficient condition for existence of spinc structures on real Bott manifolds.
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The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds
在具有任意$\Spinc$结构的紧致曲面上，我们给出了一个能量动量张量的几何表达式。给出了Dirac算子特征值的一个Bär型不等式的新证明.具有正则$\Spinc$结构的圆球$\mathbb{S}^2$满足极限情况。最后，我们通过求解与$\mathbb{S}^2\times \mathbb{R}$上的诱导$\Spinc$结构相关的广义Killing旋量方程，给出了$\mathbb{S}^2\times \mathbb{R}$中浸没曲面的旋量特征
Parallal Spinors on Pseudo-Riemannian SpinC Manifolds
我们用和乐群描述了所有单连通的不可约非局部对称伪Riemann SpinC流形，它们具有平行旋量。所以我们推广了黎曼情形和伪黎曼情形。
SpinC quantization in odd dimensions
我们定义和讨论的SpinC量子化的概念，奇维流形的扩展。之后，我们描述了它与（通常的）偶数维SpinC量子化的关系，以及如何在奇数维中恢复其著名的性质，如“量子化与还原交换”。最后，我们分析了三维流形上的情形，并给出了一些例子。
Parallel Spinors on Pseudo-Riemannian Spin C Manifolds
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The first time that the connection between isometric immersion of surfaces and solutions of the Dirac equation appeared in the literature was in the seminal paper of Thomas Friedrich in 1998. In consequence of that, several authors contributed to this topic hereafter, by obtaining the spinorial representation of Spin manifolds with arbitrary dimension and also by presenting a generalization of the Weierstrass representation map, for example. All these results assume that the manifolds and bundles involved carry a Spin structure, however this hypothesis is somehow restrictive, as for instance, …
Exact triangles in Seiberg-Witten Floer theory. Part IV: Z-graded monopole homology
讨论了具有非平凡有理同调流形的SW弗洛尔同调的构造问题。特别是，流形的情况下，得到的零外科手术的结在一个同调球，并扭转spinc结构。讨论了扭转旋结构的相对不变式。
Seiberg-Witten-Floer Homology and Gluing Formulae
本文给出了具有无挠$\spinc$结构的闭定向三维流形的Seiberg-Witten-弗洛尔同调的详细构造.得到了沿嵌入三维流形分裂的四维流形的胶合公式。
For a compact spinc manifold $X$ with boundary $b_1(\partial X)=0$, we consider moduli spaces of solutions to the Seiberg-Witten equations in a generalized double Coulomb slice in $L^2_1$ (i.e., $W^{1,2}$) Sobolev regularity. We prove they are Hilbert manifolds, prove denseness and "semi-infinite-dimensionality" properties of the restriction to $\partial X$, and establish a gluing theorem. To achieve these, we prove a general regularity theorem and a strong unique continuation principle for Dirac operators, and smoothness of a restriction map to configurations of higher regularity on the inter…
Cohomological rigidity of real Bott manifolds
实Bott流形是从一点开始的迭代RP ^1丛的全空间，其中每个RP ^1丛是两个实线丛的Whitney和的投影化。证明了两个实Bott流形是同构的，如果它们的系数为Z/2的上同调环是同构的.一个实Bott流形是一个实环面流形，并且在初等交换2-群的自然作用下有一个平坦的黎曼度量不变量。我们还证明了相反的情况也是成立的，即在初等交换2-群的作用下存在平坦黎曼度量不变量的实环面流形是实Bott流形。
Morse-Bott inequalities for manifolds with boundary
本文定义了带边界流形上的Morse-Bott函数，它是Morse函数的推广，并证明了这类流形上的Morse-Bott不等式。
Eigenvalues of vector fields, Bott's residue formula and integral invariants
给定紧致连通殆复流形上的相容向量场，本文证明了该向量场的零点集之间的特征值重数有密切的关系.我们突出了一个特殊的情况下，我们的结果，并重新解释它作为一个消失型的结果在著名的Atiyah-Bott-Singer本地化公式的框架。这种新的观点，通过陈-魏尔理论和加强版本的博特的留数公式观察到的Futaki和森田，可以导致一个障碍Killing真正的全纯向量场在紧凑的埃尔米特流形的曲率积分。
Spin-structures on real Bott manifolds with Kähler structures
设M是具有Kähler结构的实Bott流形.利用Ishida刻画给出了M上自旋结构存在的充要条件。在证明中，我们使用Popko，Szczepaenski“Cohomological rigity of oriented Hantzsche-Wendt manifolds”（Adv. Math. 302（2016），1044 - 1068）和特征类中开发的技术。
Bigraded notions of formality and Aeppli-Bott-Chern-Massey products
本文定义复流形微分形式代数的双分次形式性，并研究其与高阶 Aeppli–Bott–Chern–Massey 乘积的关系，证明低次乘积可非平凡拉回到沿复子流形的爆破。
Aeppli and Bott-Chern cohomology for bi-generalized Hermitian manifolds and $d'd''$-lemma
定义了双广义复流形的Aeppli和Bott-Chern上同调，并证明了紧致双广义Hermitian流形的Aeppli和Bott-Chern上同调是有限维的.对于完全有界的二重复形$(A, d', d'')$，我们证明了$d'd''$ -引理的有效性等价于几个上同调群具有相同的维数.给出了一类双广义Hermitian流形的Bott-Chern上同调群的一些计算。
Let $M$ be a real Bott manifold with Kähler structure. Using Ishida characterization \cite{I11} we give necessary and sufficient condition for the existence of the spin-structure on $M$. In proof we use the technic developed in \cite{PS16} and characteristic classes.
Let $(M,J,g,ω)$ be a Kähler manifold. We prove a $W^{1,2}$ weak Bott-Chern decomposition and a $W^{1,2}$ weak Dolbeault decomposition, following the $L^2$ weak Kodaira decomposition on Riemannian manifolds. Moreover, if the Kähler metric is complete and the sectional curvature is bounded, the $W^{1,2}$ Bott-Chern decomposition is strictly related to the space of $W^{1,2}$ Bott-Chern harmonic forms, i.e., $W^{1,2}$ smooth differential forms which are in the kernel of an elliptic differential operator of order $4$, called Bott-Chern Laplacian. We also generalize to the non compact case the well …
The $L^2-$Atiyah-Bott-Lefschetz theorem on manifolds with conical singularities. A heat kernel approach
利用基于热核的方法，证明了具有锥奇点的紧致流形上锥微分算子椭圆复形的$L^2-$ Lefschetz数的Atiyah-Bott-Lefschetz定理.然后，我们将我们的结果的情况下的德拉姆复杂。
Bottom spectrum and parabolicity of 3-manifolds with scalar curvature lower bound
研究具有标量曲率下界的三维流形，通过必要拓扑假设，得出底部谱精确上界及流形在特定标量曲率条件下无正格林函数这两个全局结果。
In the Stiefel manifold $X_{n,k}$, we replace Frankel linear height function by a quadratic one. We prove this is still a Morse-Bott function, whose structure of critical levels presents a dichotomy according to the sign of $n-2k$. The critical submanifolds are no longer Grassmannians but total spaces of fibrations of basis a product of two Grassmannians. We explicitly integrate the gradient flow.
We give an explicit description of the Bott-Chern cohomology groups of a compact Vaisman manifold in terms of the basic cohomology. We infer that the Bott-Chern numbers and the Dolbeault numbers of a Vaisman manifold determine each other. On the other hand, we show that the cohomological invariants $Δ^k$ introduced by Angella-Tomassini are unbounded for Vaisman manifolds. Finally, we give a cohomological characterization of the Dolbeault and Bott-Chern formality for Vaisman metrics.
Topology of iterated $S^1$-bundles
本文研究了迭代$S^1$ -丛的全空间会产生什么样的流形。在\cite{CMO}、\cite{KM}和\cite{KN}中研究的一个真实的Bott塔是迭代$S^1$ -丛的一个例子。我们证明了迭代$S^1$ -丛的全空间同胚于亚零流形。一个实博特流形，它是一个实博特塔的全空间，提供了一个闭平坦黎曼流形的例子。我们还证明了实Bott流形是唯一由迭代$\bbr{P}^1$ -丛得到的闭平坦黎曼流形。最后，我们分类了三维迭代$S^1$ -丛全空间的同胚类型。
Bott manifolds with vanishing Futaki invariants for all Kähler classes
本文证明了Futaki不变量对所有Kähler类消失的Bott流形必为射影直线乘积，刻画了此类流形的结构。
Let $(X,J,ω)$ be a compact $2n$-dimensional almost Kähler manifold. We prove primitive decompositions for Bott-Chern and Aeppli harmonic forms in special bidegrees and show that such bidegrees are optimal. We also show how the spaces of primitive Bott-Chern, Aeppli, Dolbeault and $\partial$-harmonic forms on $(X,J,ω)$ are related.
We provide a new cohomological obstruction to the existence of astheno-Kahler metrics, and study relevant examples.
On Bott-Chern and Aeppli cohomologies of almost complex manifolds and related spaces of harmonic forms
本文在近复流形上引入由d、d^c定义的Bott-Chern与Aeppli上同调推广，阐明其与已有上同调及调和形式空间的关系，并证明1-形式Bott-Chern上同调在紧流形上有限维，给出可区分近复结构的不变量。
Let $(M,J,g,ω)$ be a $2n$-dimensional almost Hermitian manifold. We extend the definition of the Bott-Chern Laplacian on $(M,J,g,ω)$, proving that it is still elliptic. On a compact Kähler manifold, the kernels of the Dolbeault Laplacian and of the Bott-Chern Laplacian coincide. We show that such a property does not hold when $(M,J,g,ω)$ is a compact almost Kähler manifold, providing an explicit almost Kähler structure on the Kodaira-Thurston manifold. Furthermore, if $(M,J,g,ω)$ is a connected compact almost Hermitian $4$-manifold, denoting by $h^{1,1}_{BC}$ the dimension of the space of Bott…
Given a compact complex manifold $X$ and a integrable Beltrami differential $ϕ\in A^{0,1}(X, T_{X}^{1,0})$, we introduce a double complex structure on $A^{\bullet,\bullet}(X)$ 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 $\partial\bar{\partial}_ϕ$-lemma is studied and we show a compact complex manifold satisfying $\partial\bar{\partial}_ϕ$-lemma is formal.
The Yang-Mills flow and the Atiyah-Bott formula on compact Kahler manifolds
研究了紧致Kahler流形X上全纯向量丛E上的Yang-Mills流。沿着流动的解，我们证明了曲率$iΛF(A_t)$在$L^2$中的逼近，$L^2$是一个具有常数特征值的自同态，特征值由E.这证明了一个尖锐的下界厄米-杨-米尔斯功能，从而杨-米尔斯功能，推广到任意尺寸的公式阿蒂亚和博特首先证明黎曼曲面。进一步证明了极限丛$E_\infty$的所有X的自反扩张同构于$Gr(E)^{\star\star}$，验证了Bando和Siu的一个猜想.
Bott-Chern cohomology and q-complete domains
在研究q-完备流形的Bott-Chern和Aeppli上同调时，我们引入了上同调的Bott-Chern q-完备流形类.
Quaternionic Bott-Chern cohomology and existence of HKT metrics
我们研究了紧致超复流形上的四元数Bott-Chern上同调，并将复几何中的一些结果应用到四元数上。例如，我们证明了实维8的紧致超复流形上HKT度量存在的一个判据，类似于Teleman [35]和Angella-Dloussky-Tomassini [3]对紧致复曲面给出的判据。
It is shown that the singular set for the Yang-Mills flow on unstable holomorphic vector bundles over compact Kaehler manifolds is completely determined by the Harder-Narasimhan-Seshadri filtration of the initial holomorphic bundle. We assign a multiplicity to irreducible top dimensional components of the singular set of a holomorphic bundle with a filtration by saturated subsheaves. We derive a singular Bott-Chern formula relating the second Chern form of a smooth metric on the bundle to the Chern current of an admissible metric on the associated graded sheaf. This is used to show that the mu…
We study the Kähler geometry of stage n Bott manifolds, which can be viewed as $n$-dimensional generalizations of Hirzebruch surfaces. We show, using a simple induction argument and the generalized Calabi construction from [ACGT04,ACGT11], that any stage n Bott manifold $M_n$ admits an extremal Kähler metric. We also give necessary conditions for $M_n$ to admit a constant scalar curvature Kähler metric. We obtain more precise results for stage 3 Bott manifolds, including in particular some interesting relations with c-projective geometry and some explicit examples of almost Kähler structures. …
Curvature of the Virasoro-Bott group
考虑流形到黎曼流形的所有嵌入的无穷维流形上的一个自然黎曼度量，在$\Emb(\Bbb R,\Bbb R)$情形下导出了它的测地线方程，结果证明它是Burgers方程.然后我们导出了无限维李群上右不变黎曼度量的测地线方程、曲率和Jacobi方程，并将其应用于$\Diff(\Bbb R)$、$\Diff(S^1)$和Virasoro-Bott群.这些结果中有许多是众所周知的，重点是简明和清晰。
Aeppli-Bott-Chern Massey products on non-Kähler solvmanifolds
本文研究了非卡拉维叶溶菌体上非平凡三重ABC-Massey积的显式计算，并证明了特定流形具有非消失的三重积且不具有近卡拉维叶度量。
Weighted Bott-Chern and Dolbeault cohomology for LCK-manifolds with potential
局部共形Kahler（LCK）流形是覆盖上具有Kahler结构的复流形，其甲板变换群通过全纯同态作用于它.我们可以把LCK流形看作是一个具有Kahler形式的复流形，其值在局部系统$L$中，称为共形权丛。$M$的$L$值上同调称为Morse-Novikov上同调。证明了Morse-Novikov复形满足$dd^c$ -引理（就像Kahler流形一样）。如果是真的，它将对LCK流形的几何产生深远的影响。Vaisman流形上Morse-Novikov $dd^c$引理的反例是由R.后藤我们证明了$dd^c$ -引理在任何具有势的LCK流形（包括Vaisman流形）上的系数在$L$的充分一般幂$L^a$中成立.我们还证明了$L^a$中系数的Dolbeault和Bott-Chern上同调为零。同样的论点被用来证明退化的Dolbeault-Frohlicher谱序列的系数在任何权力的$L$。
Quantitative and qualitative cohomological properties for non-Kähler manifolds
本文引入了复非Kähler流形的Bott-Chern上同调的一个“定性性质”，这是从研究Bott-Chern上同调的代数结构出发的.我们证明了这样一个性质刻画了$\partial\overline\partial$ -引理的有效性。这是从Bott-Chern上同调的定量研究得出的。在这方面，我们还证明了一个新的限制的维数的Bott-Chern上同调的Hodge数。我们也给出了这个上界的推广，并应用到辛上同调。
Bott Connection and Generalized Functions on Poisson Manifold
本文将寻找泊松流形上哈密顿不变体积形式的问题推广到构造哈密顿不变广义函数的问题。为此，我们引入了广义中心的泊松代数，这是广义Casimir函数的空间的概念。我们研究了当广义函数的测试对象集是紧支撑的光滑函数空间时的情形，以及当测试对象是n-形式时的情形，其中n是Poisson流形的维数。我们描述了这个问题与泊松结构的同调性质的关系，与相应的辛叶理和模类的Bott连接。
On manifolds homeomorphic to spheres
本文在Morse-Bott函数背景下证明了类似Reeb定理的结论，指出具有两个不同维数临界子流形的闭光滑流形必同胚于标准球面，并将此结果推广至实数、复数和四元数上的射影空间。
The cohomologies of the Iwasawa manifold and of its small deformations
证明了对于某些复零流形，Bott-Chern上同调完全由具有诱导复结构的零流形所对应的李代数决定.我们使用这些工具来计算岩泽流形及其小变形的Bott-Chern和Aeppli上同调，完成了M.施韦策
We prove that on a compact almost Hermitian 4-manifold the space of $\bar\partial$-harmonic $(1,1)$-forms always has dimension $h_{\bar\partial}^{1,1} = b_- +1$ or $b_-$, whilst the space of Bott-Chern harmonic $(1,1)$-forms always has dimension $h_{BC}^{1,1} = b_- +1$. We also perform calculations of $h^{2,1}_{BC}$ and $h^{1,2}_{BC}$ on the Kodaira-Thurston manifold, thereby providing a full account of when $h^{p,q}_{BC}$ is or is not invariant of the choice of almost Hermitian metric. Finally, we introduce a decomposition of the space of $L^2$ functions on all torus bundles over $S^1$, which…
The $L^2$ Aeppli-Bott-Chern Hilbert complex
本文定义了 $L^2$ Aeppli-Bott-Chern Hilbert 复形，研究其在一般 Hermitian、完备 Kähler 及 Galois 覆盖上的性质，通过自伴扩张将核与 Aeppli 或 Bott-Chern 上同调联系起来。
A $dd^Φ$-Lemma and Bott--Chern-type Cohomology for Spin(7)-Manifolds
该文研究8维无挠Spin(7)-流形上的$dd^Φ$-算子，证明其Hodge分解与类似Kähler几何的$dd^Φ$-引理，定义Bott–Chern型上同调并建立其与模空间、校准几何的关联，同时给出具有独立价值的Spin(7)结构相关恒等式。
We consider the primitive decomposition of $\bar \partial, \partial$, Bott-Chern and Aeppli-harmonic $(k,k)$-forms on compact almost Kähler manifolds $(M,J,ω)$. For any $D \in \{\bar\partial, \partial, BC, A\}$, we prove that the $L^k P^0$ component of $ψ\in \mathcal{H}_{D}^{k,k}$, is a constant multiple of $ω^k$. Focusing on dimension 8, we give a full description of the spaces $\mathcal{H}_{BC}^{2,2}$ and $\mathcal{H}_{A}^{2,2}$, from which follows $\mathcal{H}^{2,2}_{BC}\subseteq\mathcal{H}^{2,2}_{\partial}$ and $\mathcal{H}^{2,2}_{A}\subseteq\mathcal{H}^{2,2}_{\bar\partial}$. We also provi…
In this note, we show that for a closed almost-Kähler manifold $(X,J)$ with the almost complex structure $J$ satisfies $\dim\ker P_{J}=b_{2}-1$ the space of de Rham harmonic forms is contained in the space of symplectic-Bott-Chern harmonic forms. In particular, suppose that $X$ is four-dimension, if the self-dual Betti number $b^{+}_{2}=1$, then we prove that the second non-HLC degree measures the gap between the de Rham and the symplectic-Bott-Chern harmonic forms.
Integral Bott--Chern cohomology of Generalized Calabi--Eckmann threefolds
本文计算了复维3的广义Calabi--Eckmann流形的整Bott--Chern上同调，证明非双全纯流形间该上同调环同构，并用特征映射区分不同上同调。
Bottom Spectrum Estimate Under Curvature Integrability Condition
本文证明了在 Ricci 曲率具有积分意义下界的流形上，Laplacian 底谱的上界，其论证依赖于最小正 Green 函数的存在性及其性质。
Autour de la cohomologie de Bott-Chern
回忆录的目标是发展一个新的上同调理论，其中包括德拉姆和Dolbeault上同调以及德利涅贝林森上同调，在一般复杂的解析流形的背景下。岩泽流形的特殊情况进行了研究，作为一个典型的例子发生在非凯勒的情况。给出了Kodaira-Spencer形变理论和计算陈类的初步应用。
We construct non-vanishing steady solutions to the Euler equations (for some metric) with analytic Bernoulli function in each three-manifold where they can exist: graph manifolds. Using the theory of integrable systems, any admissible Morse-Bott function can be realized as the Bernoulli function of some non-vanishing steady Euler flow. This can be interpreted as an inverse problem to Arnold's structure theorem and yields as a corollary the topological classification of such solutions. Finally, we prove that the topological obstruction holds without the non-vanishing assumption: steady Euler fl…
Adiabatic limit and connections in Finsler Geometry
本文将Finsler流形的射影球面丛的自然叶理上的Bott联络等价于该流形的Chern联络。因此，Bott联络的对称化结果是Finsler流形的Cartan联络。继刘-张\cite{LiuZ}之后，Cartan联络也可以通过绝热极限过程得到。进一步定义了一个Chern-Simons型，并讨论了它的共形性质.
We give explicit harmonic representatives of Dolbeault cohomology of Oeljeklaus-Toma manifolds and show that they are geometrically Dolbeault formal. We also give explicit harmonic representatives of Bott-Chern cohomology of Oeljeklaus-Toma manifolds of type $(s,1)$ and study the Angella-Tomassini inequality.
It was conjectured by Bott-Grove-Halperin that a compact simply connected Riemannian manifold $M$ with nonnegative sectional curvature is rationally elliptic. We confirm this conjecture under the stronger assumption that $M$ has entire Grauert tube,i.e.,$M$ is a real analytic Riemannian manifold that has a unique adapted complex structure defined on the whole tangent bundle $TM$.
Non-Kähler Calabi-Yau manifolds
本文研究了一类紧致复流形，其第一个Chern类在Bott-Chern上同调中为零。这类流形包括所有具有挠典范丛的流形，但它严格较大。在作了一些基本的说明之后，我们证明了第一Bott-Chern类为零的Fujiki类C中的流形有挠典范丛。我们还给出了非Kahler Calabi-Yau流形的一些例子，并讨论了在它们上定义和构造典范度量的问题。
For every positive integer $r$, we introduce two new cohomologies, that we call $E_r$-Bott-Chern and $E_r$-Aeppli, on compact complex manifolds. When $r=1$, they coincide with the usual Bott-Chern and Aeppli cohomologies, but they are coarser, respectively finer, than these when $r\geq 2$. They provide analogues in the Bott-Chern-Aeppli context of the $E_r$-cohomologies featuring in the Frölicher spectral sequence of the manifold. We apply these new cohomologies in several ways to characterise the notion of page-$(r-1)$-$\partial\bar\partial$-manifolds that we introduced very recently. We also…
Morse-type inequalities are given for the symplectic versions of the Bott-Chern and Aeppli cohomology groups defined by Tseng and Yau.
Morse-Novikov cohomology of locally conformally Kähler manifolds
局部共形Kahler（LCK）流形是一个具有Kahler覆盖的复流形，其中单值映射通过同素映射作用于该覆盖上。我们定义了三个上同调不变量，李类，Morse-Novikov类和Bott-Chern类，LCK结构。这些不变量一起扮演着与Kahler几何中的Kahler类相同的角色。如果两个LCK结构的这些类重合，则这些结构之间的差异可以由光滑势表示，类似于Kahler的情况。我们证明了Vaisman流形的Morse-Novikov类和Bott-Chern类为零。此外，对于Vaisman流形上的任何LCK-结构，我们证明了它的Morse-Novikov类为零。证明了Bott-Chern类为零的紧致LCK-流形$M$在Hopf流形上有一个全纯嵌入，如果$\dim_\C M \geq 3$，这一结果与Kodaira嵌入定理相似.
Vaisman manifolds with vanishing first Chern class
本文研究了第一陈类消失的紧致Vaisman流形，证明具有非正Bott-Chern类的流形具有典范度量、拟正则性及形变稳定性，并指出Calabi-Yau Vaisman流形满足Beauville-Bogomolov分解且具有挠典范丛。
Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds
本文研究了圈作用下哈密顿函数的虚拟Morse-Bott指数，证明其与经典Morse-Bott指数一致，并利用Hirzebruch-Riemann-Roch定理计算了所有临界层的虚拟指数，验证了四维光滑流形的Bogomolov-Miyaoka-Yau不等式猜想。
On the $\partial\overline{\partial}$-Lemma and Bott-Chern cohomology
在紧致复流形$X$上，证明了Bott-Chern上同调的Frölicher型不等式，并证明了该不等式成立的充要条件是$X$满足$\partial\overline{\partial}$ -引理.
Our goal in this work is to develop aspects of Bialynicki-Birula and Morse-Bott theory that can be extended from the classical setting of smooth manifolds to that of complex analytic spaces with a holomorphic $\mathbb{C}^*$ action. We extend prior results on existence of Bialynicki-Birula decompositions for compact, complex Kähler manifolds to non-compact complex manifolds and develop functorial properties of the Bialynicki-Birula decomposition, in particular with respect to blowup along a $\mathbb{C}^*$-invariant, embedded complex submanifold. We deduce the existence of a Bialynicki-Birula de…
Topology of locally conformally Kahler manifolds with potential
局部共形Kahler（LCK）位势流形是那些允许一个Kahler覆盖有一个真的自守Kahler位势的流形。一个势函数的存在性可以上同调地描述为某个上同调类的消失，这个上同调类称为Bott-Chern类。具有位势的紧致LCK流形在小变形下是稳定的，并且允许全纯嵌入到Hopf流形中。这个类严格包括Vaisman流形。我们证明了每一个具有位势的紧致LCK流形都可以变形为Vaisman流形。因此，每一个这样的流形都是Kahler orbifold上的光滑椭圆纤维化。我们证明了G. Kokarev等价于Bott-Chern类的消失。这给出了一个简单的证明的一些结果拓扑的pluricanonical LCK-流形，发现的Kokarev和Kotschick。
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