论文标题
Lagrangian交叉点和广义共同体理论中
Lagrangian intersections and cuplength in generalised cohomology theories
论文作者
论文摘要
我们发现两个相对精确的哈密顿同位素拉格朗日人之间的交叉点数量的下限。界限是根据拉格朗日在各种乘法广义的共同体学理论中的cuplength提出的。 Lagrangians的交集不必横向，但是，我们需要某些方向假设。这比以前的估计值对合适的闭合，相对精确的拉格朗日差异的自我交流点的估计值更强。我们的证明使用Lusternik-Schnirelmann理论，遵循Hofer的工作并扩展了工作。
We find lower bounds on the number of intersection points between two relatively exact Hamiltonian isotopic Lagrangians. The bounds are given in terms of the cuplength of the Lagrangian in various multiplicative generalised cohomology theories. The intersection of the Lagrangians need not be transverse, however, we require certain orientation assumptions. This gives stronger bounds than previous estimates on the number of self-intersection points of a suitable closed, relatively exact Lagrangian diffeomorphic to Sp$(2)$ or Sp$(3)$. Our proof uses Lusternik-Schnirelmann theory, following and extending work by Hofer.
