发表机构
Universität Hamburg（汉堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文在派生叠上证明移位接触Thurston定理，即若态射具有移位恰当辛纤维化结构且基底有移位接触结构，则源叠也有相容的移位接触结构，并给出余法叠等应用。
AI 中文摘要
在经典接触几何的框架内，第一作者引入了接触辛结构的概念——即具有接触基底的恰当辛纤维化的数据——并在温和条件下证明了此类纤维化的全空间继承了一个与纤维化映射相容的接触结构，从而确立了接触Thurston定理。本文通过结合我们先前关于派生辛Thurston定理的工作，提供了该结果的派生接触版本。在本文中，我们证明了在特定条件下，如果派生叠的态射$\pi: X \rightarrow S$具有移位恰当辛纤维化结构，且目标叠$S$允许移位接触结构，那么可以在源叠$X$上构造一个移位接触结构，该结构与$\pi$相容，其相容方式类似于光滑情形。我们的框架依赖于相对移位结构的理论；因此，我们的结果称为派生接触Thurston定理，实际上建立了一种从相对到绝对的构造类型。作为应用，我们在派生接触环境中展示了相对到绝对构造形式化的例子，包括余法叠、商映射叠和仿射恰当辛纤维化。
英文摘要
Within the framework of classical contact geometry, the first author introduced the notion of contact symplectic structure --the data of an exact symplectic fibration with a contact base-- and proved, under mild conditions, that the total space of such a fibration inherits a contact structure compatible with the fibration map, thereby establishing the contact Thurston theorem. This paper provides a derived contact version of that result by incorporating our prior work on the derived symplectic Thurston theorem. In this paper, we prove, under certain conditions, that if a morphism $π: X \rightarrow S$ of derived stacks has a shifted exact symplectic fibration structure and the target stack $S$ admits a shifted contact structure, then one can construct a shifted contact structure on the source stack $X$, compatible with $π$ in a sense similar to the smooth case. Our framework relies on the theory of relative shifted structures; hence our result, called the derived contact Thurston theorem, in fact establishes a relative-to-absolute type construction. As an application, we present examples of our relative-to-absolute construction formalism in the derived contact setting, including conormal stacks, quotient mapping stacks, and affine exact symplectic fibrations.
Comments27 pages. Comments are welcome!
