论文标题
Reeb轨道的局部符号同源性
Local Symplectic Homology of Reeb Orbits
论文作者
论文摘要
在本文中，我们证明了简单的局部符号同源性中的两个同构，即未迭代的，孤立的Reeb轨道。同构为$ s^1 $ equivariant和非quivariant symphectic同源性，将轨道的本地浮子同源组与返回图的轨道相关。我们在$ s^1 $ - equivariant sympletic同源性中证明的同构可以简洁地说明，因为简单孤立的Reeb轨道的本地$ s^1 $ equivariant符号符合性同源性是对返回图的本地汉密尔顿浮球同源物的同构。我们还证明了Reeb轨道的两个不同定义的等效性是符合性归化的最大值。
In this paper we prove two isomorphisms in the local symplectic homology of a simple, which is to say non iterated, isolated Reeb orbit. The isomorphisms are in $S^1$-equivariant and nonequivariant symplectic homology, relating the local Floer homology group of the orbit to that of the return map. The isomorphism we prove in $S^1$-equivariant symplectic homology can be stated succinctly as the local $S^1$-equivariant symplectic homology of a simple isolated Reeb orbit is isomorphic to the local Hamiltonian Floer homology of the return map. We also prove the equivalence of two different definitions of a Reeb orbit being a symplectically degenerate maximum.
