论文标题
$ s^1 $ equivariant同源性和弦拓扑应用的共生结构
A cocyclic construction of $S^1$-equivariant homology and application to string topology
论文作者
论文摘要
鉴于具有圆形动作的空间，我们本着琼斯著名的作品的精神，研究了某些Cocyclic链复合物，并证明了与$ s^1 $ equivariant同源性相关的定理。作为应用程序，我们根据Irie在链条级别的弦乐拓扑的工作和Ward在$ s^1 $ -S^1 $ quarivariant版本的Operadic Deligne的Jumpolatiant版本上的工作，描述了重力代数结构的链级改进（负）$ s^1 $ equivariant同源性。
Given a space with a circle action, we study certain cocyclic chain complexes and prove a theorem relating cyclic homology to $S^1$-equivariant homology, in the spirit of celebrated work of Jones. As an application, we describe a chain level refinement of the gravity algebra structure on the (negative) $S^1$-equivariant homology of the free loop space of a closed oriented smooth manifold, based on work of Irie on chain level string topology and work of Ward on an $S^1$-equivariant version of operadic Deligne's conjecture.
