论文标题
联络流量同源性中的哈密顿扰动
Hamiltonian perturbations in contact Floer homology
论文作者
论文摘要
我们研究了由Mermer-Uljarević引入的Contact Floer同源性$ {\ rm Hf} _*（W，H）$，该$将浮动型同源性理论与Liouville域$ W $和接触汉密尔顿$ H $相关联。主要结果调查了在输入联系人汉密尔顿$ h $的扰动下$ {\ rm hf} _*（w，h）$的行为。特别是，我们提供了足够的条件，可以保证$ {\ rm hf} _*（w，h）$在扰动下不变。这可以被视为沿着Hamiltonian Floer同源物中的Hamiltonian扰动的延续和分叉图的接触几何类似物。作为应用程序，我们给出了一个代数证明，证明了有关广泛的接触歧管的接触符号的正循环的刚性结果。
We study the contact Floer homology ${\rm HF}_*(W, h)$ introduced by Merry-Uljarević, which associates a Floer-type homology theory to a Liouville domain $W$ and a contact Hamiltonian $h$ on its boundary. The main results investigate the behavior of ${\rm HF}_*(W, h)$ under the perturbations of the input contact Hamiltonian $h$. In particular, we provide sufficient conditions that guarantee ${\rm HF}_*(W, h)$ to be invariant under the perturbations. This can be regarded as a contact geometry analogue of the continuation and bifurcation maps along the Hamiltonian perturbations of Hamiltonian Floer homology in symplectic geometry. As an application, we give an algebraic proof of a rigidity result concerning the positive loops of contactomorphisms for a wide class of contact manifolds.
