论文标题
降低：预配合与前链
Reductions: precontact versus presymplectic
论文作者
论文摘要
我们表明，可以用传统的Marsden-Weinstein-Meyer以及恒定的等级图片来描述接触降低。关键是我们将接触结构视为特定的（均质）符号结构。通过接触型的小组作用将哈密顿对相应的象征性歧管的作用提升为称为触点歧管的符号掩护。与该主题中的大多数文献相反，我们的方法包括一般的接触结构（不仅是共同定位），并改变了传统的观点：接触式触摸态构成组的触点和接触力矩图不再在接触歧管本身上定义，而且在其符号覆盖范围内不再定义。实际上，开发的减少框架比纯粹的接触框架稍微泛滥，其中包括一个预性和完整的设置，该设置基于以下观察到的，即在预先歧管的同构类别和某些均质的均质前歧管之间存在一对一的对应关系。
We show that contact reductions can be described in terms of symplectic reductions in the traditional Marsden-Weinstein-Meyer as well as the constant rank picture. The point is that we view contact structures as particular (homogeneous) symplectic structures. A group action by contactomorphisms is lifted to a Hamiltonian action on the corresponding symplectic manifold, called the symplectic cover of the contact manifold. In contrast to the majority of the literature in the subject, our approach includes general contact structures (not only co-oriented) and changes the traditional view point: contact Hamiltonians and contact moment maps for contactomorphism groups are no longer defined on the contact manifold itself, but on its symplectic cover. Actually, the developed framework for reductions is slightly more general than purely contact, and includes a precontact and presymplectic setting which is based on the observation that there is a one-to-one correspondence between isomorphism classes of precontact manifolds and certain homogeneous presymplectic manifolds.
