A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY
A CONTACT INVARIANT IN SUTURED MONOPOLE HOMOLOGY
复制标题
缝合单极同调中的接触不变量
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Steven Sivek
中科院分区：
文献类型：
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作者：
John A. Baldwin;Steven Sivek
利用Kronheimer和Mrowka的缝合单极Floer同调理论($SHM)定义了具有凸边界的接触三维流形的一个不变量。我们的不变量可以看作是闭接触三维流形上Kronheimer和Mrowka的接触不变量的推广，也可以看作是ć，Kazez和Mati Heegaard Floer同调($SFH$)中Honda，Kazez和Mati Heegaard Floer同调中的单极点Floer不变量的类似.在定义不变量的过程中，我们在与联系人句柄附件相关联的$shm$上构造映射，类似于Honda、Kazez和Matić在$SFH$中定义的映射。我们使用这些地图在$SHM$中建立一个绕过精确三角形，类似于本田在$SFH$中的三角形。本文还为在Baldwin和Sivek[Selecta Math]中使用的缝合瞬子Floer同调中的类胶合映射的构造提供了拓扑基础。(N.S.)，22(2)(2016)，939-978]来定义瞬动子Floer设置中的触点不变量。
We define an invariant of contact 3-manifolds with convex boundary using Kronheimer and Mrowka’s sutured monopole Floer homology theory ( $SHM$ ). Our invariant can be viewed as a generalization of Kronheimer and Mrowka’s contact invariant for closed contact 3-manifolds and as the monopole Floer analogue of Honda, Kazez, and Matić’s contact invariant in sutured Heegaard Floer homology ( $SFH$ ). In the process of defining our invariant, we construct maps on $SHM$ associated to contact handle attachments, analogous to those defined by Honda, Kazez, and Matić in $SFH$ . We use these maps to establish a bypass exact triangle in $SHM$ analogous to Honda’s in $SFH$ . This paper also provides the topological basis for the construction of similar gluing maps in sutured instanton Floer homology, which are used in Baldwin and Sivek [Selecta Math. (N.S.), 22(2) (2016), 939–978] to define a contact invariant in the instanton Floer setting.