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Cosimplicial Objects and little n-cubes. I | | James E. McClure
; Jeffrey H. Smith
; | | Date: |
23 Nov 2002 | | Subject: | Quantum Algebra; Algebraic Topology MSC-class: 18D50; 55P48 | math.QA math.AT | | Abstract: | In this paper we show that if a cosimplicial space or spectrum $X^ullet$ has a certain kind of combinatorial structure (we call it a $Xi^n$-structure) then the total space of $X^$ has an action of a certain operad which is weakly equivalent to the little n-cubes operad. The $nleq 2$ 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 $n=infty$, we define a symmetric monoidal structure $oxtimes$ on cosimplicial spaces and show that if $X^$ is a commutative $oxtimes$-monoid then the total space of $X^$ is an $E_infty$ space. | | Source: | arXiv, math.QA/0211368 | | Services: | Forum | Review | PDF | Favorites | |
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