Dimension vs. genus: A surface realization of the little k-cubes and an E ∞ operad

Ralph M. Kaufmann

Banach Center Publications (2009)

  • Volume: 85, Issue: 1, page 241-274
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Ralph M. Kaufmann. "Dimension vs. genus: A surface realization of the little k-cubes and an $E_{∞}$ operad." Banach Center Publications 85.1 (2009): 241-274. <http://eudml.org/doc/281802>.

@article{RalphM2009,
abstract = {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.},
author = {Ralph M. Kaufmann},
journal = {Banach Center Publications},
keywords = {operads; moduli of surfaces; little cubes; Dyer-Lashof operations},
language = {eng},
number = {1},
pages = {241-274},
title = {Dimension vs. genus: A surface realization of the little k-cubes and an $E_\{∞\}$ operad},
url = {http://eudml.org/doc/281802},
volume = {85},
year = {2009},
}

TY - JOUR
AU - Ralph M. Kaufmann
TI - Dimension vs. genus: A surface realization of the little k-cubes and an $E_{∞}$ operad
JO - Banach Center Publications
PY - 2009
VL - 85
IS - 1
SP - 241
EP - 274
AB - 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.
LA - eng
KW - operads; moduli of surfaces; little cubes; Dyer-Lashof operations
UR - http://eudml.org/doc/281802
ER -

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