2002/11/23 by James E. McClure, McClure, James E., Jeffrey H. Smith +1 · 2 citations
Mathematics · #18D50 #55P48 #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA) #math.AT #math.QA #msc:18D50 #msc:55P48
paper · pdf · doi:10.48550/arxiv.math/0211368
There are three new sections: Section 10 shows that $Ξ^2$-structures are essentially the same thing as operads with multiplication, Section 11 shows that the operad $\cal D_n$ acts on $n$-fold loop spaces, and Section 15 shows that the main results are still valid for the homotopy-invariant version of Tot
openalex publication_date 2002/11/23 · arxiv created 2004/02/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we show that if a cosimplicial space or spectrum X^\bullet has a certain kind of combinatorial structure (we call it a Ξn-structure) then the total space of X^\b has an action of a certain operad which is weakly equivalent to the little n-cubes operad. The n≤ 2 case was proved by a more complicated argument in our earlier paper A Solution of Deligne's Hochschild Cohomology Conjecture (http://front.math.ucdavis.edu/math.QA/9910126). In the special case n=∞, we define a symmetric monoidal structure \boxtimes on cosimplicial spaces and show that if X^\b is a commutative \boxtimes-monoid then the total space of \X^\b is an E_∞ space.