Dimension vs. genus: A surface realization of the little k-cubes and an $E_{∞}$ operad

• Autorzy: Ralph M. Kaufmann
• Języki publikacji: EN

Abstrakty

EN

We define a new $E_{∞}$ operad based on surfaces with foliations which contains $E_k$ suboperads. 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.

Kategorie tematyczne

• 32G15: Moduli of Riemann surfaces, Teichm\"uller theory
• 55P35: Loop spaces
• 16E40: (Co)homology of rings and algebras (e.g. Hochschild, cyclic, dihedral, etc.)
• 55P48: Loop space machines, operads
• 18D50: Operads

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2009
• Tom: 85
• Numer: 1
• Strony: 241-274

Daty

wydano

2009

Twórcy

autor

Ralph M. Kaufmann

• Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN 47907-2067, U.S.A.

Identyfikatory

DOI

10.4064/bc85-0-17