论文标题
选择性符号同源性，并应用于与非平方联系
Selective symplectic homology with applications to contact non-squeezing
论文作者
论文摘要
我们证明了在同质球上的触点非平衡现象，该领域由具有无限尺寸符号符号同源性的liouville域填充：在这样的球体中存在一个平滑的嵌入球，而不能通过触点同位素进行任意地使其较小。这些同质验证领域包括对标准球的差异且其接触结构与标准接触结构同型的示例。作为主要工具，我们构建了一种新版本的符号同源性，称为选择性符号同源性，该学与liouville域和其边界的开放子集有关。选择性符号同源性是作为对汉密尔顿人的浮球同源组的直接极限，其斜坡倾向于在开放子集中无穷大，但保持接近0，并且在边界的其余部分上保持阳性。
We prove a contact non-squeezing phenomenon on homotopy spheres that are fillable by Liouville domains with infinite dimensional symplectic homology: there exists a smoothly embedded ball in such a sphere that cannot be made arbitrarily small by a contact isotopy. These homotopy spheres include examples that are diffeomorphic to standard spheres and whose contact structures are homotopic to standard contact structures. As the main tool, we construct a new version of symplectic homology, called selective symplectic homology, that is associated to a Liouville domain and an open subset of its boundary. The selective symplectic homology is obtained as the direct limit of Floer homology groups for Hamiltonians whose slopes tend to infinity on the open subset but remain close to 0 and positive on the rest of the boundary.
