稳定映射类群上的无限闭路空间结构
Infinite loop space structure(s) on the stable mapping class group
摘要：
Tillmann在稳定映射类群的分类空间的加法构造上引入了两种无限闭路空间结构，它们具有不同的计算优势。第一种方法是在一个合适的配边范畴上使用不交并，而第二种方法是使用一个操作数，它扩展了裤子乘法（即E. Y. Miller）。她解释说这两个无限闭路空间结构是等价的，并设法证明了第一个去环是相同的。在本文中，我们解决了猜想证明这两个结构确实是等价的，表现出一个明确的几何映射。
英文摘要：
Tillmann introduced two infinite loop space structures on the plus construction of the classifying space of the stable mapping class group, each with different computational advantages. The first one uses disjoint union on a suitable cobordism category, whereas the second uses an operad which extends the pair of pants multiplication (i.e. the double loop space structure introduced by E. Y. Miller). She conjectured that these two infinite loop space structures were equivalent, and managed to prove that the first delooping are the same. In this paper, we resolve the conjecture by proving that the two structures are indeed equivalent, exhibiting an explicit geometric map.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
