论文标题
弯曲的绝对同义谎言代数的整合理论
The integration theory of curved absolute homotopy Lie algebras
论文作者
论文摘要
本论文的主要目标是发展曲面同喻的整合理论在代数中。在第一章中，我们开发了所需的经营微积分：我们用歌剧编码非必要的综合山结构，并在库里引入其对代数的双重概念，我们称之为“绝对代数”。本章的第一部分是艺术的状态，最后三个部分是由原始结果组成的。在第二章中，我们开发了曲线的新理论，该理论使我们能够用弯曲的作业编码代数的弯曲类型。最后，在第三章中，我们使用前两章中介绍的工具开发了曲线绝对同义的集成理论。这种新方法使我们能够为变形理论和合理同义理论获得应用。
The main goal of this thesis is to develop the integration theory of curved homotopy Lie algebras. In the first chapter, we develop the operadic calculus needed: we encode non-necessarily conilpotent coalgebras with operads and introduce their dual notion of an algebra over a cooperad, which we call "absolute algebras". The first sections of this chapter are a state of the art, and the last three sections are made of original results. In the second chapter, we develop the new theory of curved operadic calculus, which allows us to encode curved types of algebras with curved operads. Finally, in the third chapter, we develop the integration theory of curved absolute homotopy Lie algebras using the tools introduced in the first two chapters. This new approach allows us to obtain applications to deformation theory and rational homotopy theory.
