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arXiv · 1102.1311

An Additivity Theorem for the Interchange of E_n Structures

Zbigniew Fiedorowicz·Rainer M. Vogt
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Abstract

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.

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Zbigniew Fiedorowicz, Rainer M. Vogt. 2013-11-11. An Additivity Theorem for the Interchange of E_n Structures. https://arxiv.org/abs/1102.1311

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