E_n结构互换的可加性定理
An Additivity Theorem for the Interchange of E_n Structures
摘要：
拓扑空间上两个乘法结构互换的概念由参数化这些结构的两个运算的张量积编码。因此，直觉上人们可能会认为，E_m和E_n操作数（分别编码m重和n重闭路空间的乘法结构）的张量积应该是E_{m+n}操作数。然而，对于这个天真的猜想，有一些简单的反例。本文证明了余E_m和余E_n的张量积是E_{m+n}运算。由此得出，如果A_i是E_{m_i}操作数，其中i= 1，2，.，k，则有一个E_{m_1+m_2+...+m_k}操作数映射到它们的张量积。
英文摘要：
The notion of interchange of two multiplicative structures on a topological space is encoded by the tensor product of the two operads parametrizing these structures. Intuitively one might thus expect that the tensor product of an E_m and an E_n operad (which encode the muliplicative structures of m-fold, respectively n-fold loop spaces) ought to be an E_{m+n} operad. However there are easy counterexamples to this naive conjecture. In this paper we show that the tensor product of a cofibrant E_m operad and a cofibrant E_n operad is an E_{m+n} operad. It follows that if A_i are E_{m_i} operads for i=1,2,...,k, then there is an E_{m_1+m_2+...+m_k} operad which maps into their tensor product.
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。
