Cosimplicial Objects and little n-cubes. I
| dc.creator | McClure, James E. | |
| dc.creator | Smith, Jeffrey H. | |
| dc.date | 2002-11-23 | |
| dc.date | 2004-02-07 | |
| dc.date.accessioned | 2026-07-07T04:53:14Z | |
| dc.date.available | 2026-07-07T04:53:14Z | |
| dc.description | 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 $Ξ^n$-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 $n\leq 2$ 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 $\boxtimes$ on cosimplicial spaces and show that if $X^\b$ is a commutative $\boxtimes$-monoid then the total space of $\X^\b$ is an $E_\infty$ space. | |
| dc.description | 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 | |
| dc.identifier | https://arxiv.org/abs/math/0211368 | |
| dc.identifier | http://arxiv.org/abs/math/0211368 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65763 | |
| dc.subject | Quantum Algebra | |
| dc.subject | Algebraic Topology | |
| dc.subject | 18D50; 55P48 | |
| dc.title | Cosimplicial Objects and little n-cubes. I | |
| dc.type | text |