论文标题
与地面同源性和接触结构接壤
Bordered Floer homology and contact structures
论文作者
论文摘要
我们在边界缝合的Heegaard Floer同源物中引入了一个与边界的缝合的Heegaard Floer同源性。不变的输入是触点歧管$（M，ξ，\ Mathcal {f}）$，其凸边界配备了与特征叶面密切相关的签名单数叶片$ \ Mathcal {f} $。这样的流派承认了一个由Giroux信函归类的叶状开放式书籍分解家庭，如前所述，如Licata和Vértesi的早期工作所述。我们使用一类特殊的叶面开放书籍来构建可允许的边界缝合的Heegaard图，并在相应的边界缝合模块中确定定义明确的类$ C_D $和$ C_A $。 Folieding Open Books展示了用户友好的粘合行为，我们表明，粘合兼容的叶面开放式书籍引起的不变式配对恢复了Heegaard Floer接触式的封闭触点歧管。我们还考虑了与忘记叶子$ \ Mathcal {f} $相关的自然地图，而不是分隔集，并表明它将边界缝合的不变性映射到Honda-Kazez-Matić定义的缝合流形的触点不变。
We introduce a contact invariant in the bordered sutured Heegaard Floer homology of a three-manifold with boundary. The input for the invariant is a contact manifold $(M, ξ, \mathcal{F})$ whose convex boundary is equipped with a signed singular foliation $\mathcal{F}$ closely related to the characteristic foliation. Such a manifold admits a family of foliated open book decompositions classified by a Giroux Correspondence, as described in earlier work of Licata and Vértesi. We use a special class of foliated open books to construct admissible bordered sutured Heegaard diagrams and identify well-defined classes $c_D$ and $c_A$ in the corresponding bordered sutured modules. Foliated open books exhibit user-friendly gluing behavior, and we show that the pairing on invariants induced by gluing compatible foliated open books recovers the Heegaard Floer contact invariant for closed contact manifolds. We also consider a natural map associated to forgetting the foliation $\mathcal{F}$ in favor of the dividing set, and show that it maps the bordered sutured invariant to the contact invariant of a sutured manifold defined by Honda-Kazez-Matić.
