Dimension vs. Genus: A surface realization of the little k-cubes and an E_{\infty}-operad

Details Dimension vs. Genus: A surface realization of the little k-cubes and an E_{\infty}-operad Dimension vs. Genus: A surface realization of the little k-cubes and an E_{\infty}-operad

2008-01-03

arxiv.org/abs/0801.0532v2

Mathematics

Algebraic Topology

36 pages, 15 figures, new version, some more explanations and clarifications added

Scientific paper

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.

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