Year: 2008
Type: preprint
Abstract: 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 $Ω$ spectra. The underlying novel principle is that we can trade genus in the surface representation vs. the dimension $k$ of the little $k$-cubes.
Source: arXiv (Cornell University)
Author: Kaufmann, Ralph M.
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2950726397