ORIENTATIONS IN LEGENDRIAN CONTACT HOMOLOGY AND EXACT LAGRANGIAN IMMERSIONS
ORIENTATIONS IN LEGENDRIAN CONTACT HOMOLOGY AND EXACT LAGRANGIAN IMMERSIONS
复制标题
传奇接触同调和精确拉格朗日沉浸中的方向
DOI：
10.1142/s0129167x05002941
复制
发表时间：
2004
影响因子：
0.6
通讯作者：
M. Sullivan
中科院分区：
文献类型：
--
作者：
T. Ekholm;John B. Etnyre;M. Sullivan
我们展示了如何定向模空间的全纯磁盘的边界上的一个确切的拉格朗日浸入的自旋流形到复杂的n-空间中的一个连贯的方式。这使得我们可以将标准切触（2n + 1）-空间的勒让德自旋子流形的切触同调系数从1/2提升到1/2。我们演示了如何的升降机提供了一个更精致的勒让德合痕不变量。我们还采用接触的同源性，以产生下界的双重点的某些确切的拉格朗日浸入到dogn，并再次包括方向加强的结果。更精确地说，我们证明了一个封闭的流形M的确切拉格朗日浸入的双重点的数量，其相关的勒让德嵌入有良好的DGA是至少一半的维数的同调M的系数在任意领域，如果M是自旋，否则在π 2。
We show how to orient moduli spaces of holomorphic disks with boundary on an exact Lagrangian immersion of a spin manifold into complex n-space in a coherent manner. This allows us to lift the coefficients of the contact homology of Legendrian spin submanifolds of standard contact (2n + 1)-space from ℤ2 to ℤ. We demonstrate how the ℤ-lift provides a more refined invariant of Legendrian isotopy. We also apply contact homology to produce lower bounds on double points of certain exact Lagrangian immersions into ℂn and again including orientations strengthens the results. More precisely, we prove that the number of double points of an exact Lagrangian immersion of a closed manifold M whose associated Legendrian embedding has good DGA is at least half of the dimension of the homology of M with coefficients in an arbitrary field if M is spin and in ℤ2 otherwise.