论文标题
log-symplectic歧管中拉格朗日亚曼福尔德的变形
Deformations of Lagrangian submanifolds in log-symplectic manifolds
论文作者
论文摘要
本文致力于对数 - 合成歧管的奇异轨迹中包含的拉格朗日亚曼叶的变形。我们证明了围绕这种拉格朗日的对数 - 隔离结构的正常形式结果，我们用它来提取有关拉格朗日变形的代数和几何信息。我们表明，变形问题受DGLA的约束，我们讨论了Lagrangian是否允许在奇异基因座中包含的变形，并且我们为一阶变形的毫无疑问提供了精确的标准。我们还解决了变形的等效性，表明DGLA的量规等值与哈密顿同位素的等效性的几何概念相对应。我们讨论了相应的模量空间，并证明了泊松同位素更灵活的等效关系的刚度声明。
This paper is devoted to deformations of Lagrangian submanifolds contained in the singular locus of a log-symplectic manifold. We prove a normal form result for the log-symplectic structure around such a Lagrangian, which we use to extract algebraic and geometric information about the Lagrangian deformations. We show that the deformation problem is governed by a DGLA, we discuss whether the Lagrangian admits deformations not contained in the singular locus, and we give precise criteria for unobstructedness of first order deformations. We also address equivalences of deformations, showing that the gauge equivalence relation of the DGLA corresponds with the geometric notion of equivalence by Hamiltonian isotopies. We discuss the corresponding moduli space, and we prove a rigidity statement for the more flexible equivalence relation by Poisson isotopies.
