%0 Journal Article
%T Dimension vs. Genus: A surface realization of the little k-cubes and an E_{\infty}-operad
%A Ralph M. Kaufmann
%J Mathematics
%D 2008
%I arXiv
%X We define a new $E_{\infty}$ operad based on surfaces with foliations which contains $E_k$ sub-operads. We construct CW models for these operads and provide applications of these models by giving actions on Hochschild complexes -thus making contact with string topology-, by giving explicit cell representatives for the Dyer-Lashof-Cohen operations for the 2-cubes and by constructing new $\Omega$ spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension $k$ of the little $k$-cubes.
%U http://arxiv.org/abs/0801.0532v2