论文标题
异国情调的dehn twists twists of两个接触3个manifolds的总和
Exotic Dehn twists on sums of two contact 3-manifolds
论文作者
论文摘要
我们展示了以无限顺序作为接触映射类组的元素的第一个外来接触符号的例子。这些是由某些dehn扭曲在分离球体上以两个封闭触点3个manifolds的连接总和的相关总和给出的。我们通过坚硬和软技术的结合来检测到这些。一方面，我们对接触结构的家庭进行了不变的本质，该家族将Kronheimer-Mrowka接触式触点在Monopole Floer同源性中不变。然后，我们为凸球的家族中的HO-PRINCIPLE开发了一个紧密的接触3个manifolds的家族，从中我们建立了Colin分解定理的参数版本。作为进一步的应用，我们还在公开的3个脉冲接触中表现出新的外来1-参数现象。
We exhibit the first examples of exotic contactomorphisms with infinite order as elements of the contact mapping class group. These are given by certain Dehn twists on the separating sphere in a connected sum of two closed contact 3-manifolds. We detect these by a combination of hard and soft techniques. On the one hand, we make essential use of an invariant for families of contact structures which generalises the Kronheimer--Mrowka contact invariant in monopole Floer homology. We then exploit an h-principle for families of convex spheres in tight contact 3-manifolds, from which we establish a parametric version of Colin's decomposition theorem. As a further application, we also exhibit new exotic 1-parametric phenomena in overtwisted contact 3-manifolds.
