论文标题
循环空间的Poincaré二元性
Poincaré duality for loop spaces
论文作者
论文摘要
我们表明，Rabinowitz浮子同源性和同一个同源物具有针对封闭和开放式弦的分级Frobenius代数的结构。我们证明了同源性和共同体之间的庞加莱二元定理，它保留了这种结构。这将升至分级开放闭合TQFT之间的二元定理。我们以系统的方式使用泰特矢量空间的形式主义。 我们专门针对Cotangent Bundles的情况，定义了Rabinowitz Loop同源性和协同组，并从统一的双重结果对解释，这些结果在寻找封闭的大地测量学的背景下已经观察到。这些涉及关键水平，与基于循环空间的关系，将所有大地测量的封闭式，BOTT索引迭代和级别的权利。此外，渐变的Frobenius代数结构为Sullivan在Loop产品和coproduct之间猜想的关系提供了意义和证明。
We show that Rabinowitz Floer homology and cohomology carry the structure of a graded Frobenius algebra for both closed and open strings. We prove a Poincaré duality theorem between homology and cohomology that preserves this structure. This lifts to a duality theorem between graded open-closed TQFTs. We use in a systematic way the formalism of Tate vector spaces. Specializing to the case of cotangent bundles, we define Rabinowitz loop homology and cohomology and explain from a unified perspective pairs of dual results that have been observed over the years in the context of the search for closed geodesics. These concern critical levels, relations to the based loop space, manifolds all of whose geodesics are closed, Bott index iteration, and level-potency. Moreover, the graded Frobenius algebra structure gives meaning and proof to a relation conjectured by Sullivan between the loop product and coproduct.
