弧运算与弧代数
Arc Operads and Arc Algebras
摘要：
介绍并研究了有界曲面中基于投影加权弧族的几种拓扑和同调运算。基本操作数的基础空间被确定为紧化的开子集，由于彭纳的空间密切相关的黎曼模空间。这些运算的代数被证明是Batalin-Vilkovisky代数，其中整个BV结构被简单地实现。此外，我们的基本运算包含仙人掌运算，直到同伦，它类似地作用于任何拓扑空间的闭路空间。新的操作数结构上的循环进行分类，并结合基本操作数产生几何自然扩张的代数结构的BV代数，这也计算。
英文摘要：
Several topological and homological operads based on families of projectively weighted arcs in bounded surfaces are introduced and studied. The spaces underlying the basic operad are identified with open subsets of a compactification due to Penner of a space closely related to Riemann's moduli space. Algebras over these operads are shown to be Batalin-Vilkovisky algebras, where the entire BV structure is realized simplicially. Furthermore, our basic operad contains the cacti operad up to homotopy, and it similarly acts on the loop space of any topological space. New operad structures on the circle are classified and combined with the basic operad to produce geometrically natural extensions of the algebraic structure of BV algebras, which are also computed.
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