Taylor towers for Γ -modules

Birgit Richter[1]

  • [1] Mathematisches Institut der Universität Bonn, Beringsstrasse 1, 53115 Bonn (Germany)

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 4, page 995-1023
  • ISSN: 0373-0956

Abstract

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We consider Taylor approximation for functors from the small category of finite pointed sets Γ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.

How to cite

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Richter, Birgit. "Taylor towers for $\Gamma $-modules." Annales de l’institut Fourier 51.4 (2001): 995-1023. <http://eudml.org/doc/115942>.

@article{Richter2001,
abstract = {We consider Taylor approximation for functors from the small category of finite pointed sets $\Gamma $ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.},
affiliation = {Mathematisches Institut der Universität Bonn, Beringsstrasse 1, 53115 Bonn (Germany)},
author = {Richter, Birgit},
journal = {Annales de l’institut Fourier},
keywords = {Taylor tower; cubical construction; dual of the Steenrod algebra; dual of Steenrod algebra; higher-order Hochschild homology},
language = {eng},
number = {4},
pages = {995-1023},
publisher = {Association des Annales de l'Institut Fourier},
title = {Taylor towers for $\Gamma $-modules},
url = {http://eudml.org/doc/115942},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Richter, Birgit
TI - Taylor towers for $\Gamma $-modules
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 4
SP - 995
EP - 1023
AB - We consider Taylor approximation for functors from the small category of finite pointed sets $\Gamma $ to modules and give an explicit description for the homology of the layers of the Taylor tower. These layers are shown to be fibrant objects in a suitable closed model category structure. Explicit calculations are presented in characteristic zero including an application to higher order Hochschild homology. A spectral sequence for the homology of the homotopy fibres of this approximation is provided.
LA - eng
KW - Taylor tower; cubical construction; dual of the Steenrod algebra; dual of Steenrod algebra; higher-order Hochschild homology
UR - http://eudml.org/doc/115942
ER -

References

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  1. A.K. Bousfield, E.M. Friedlander, Homotopy theory of Γ -spaces, spectra, and bisimplicial sets, 658 (1978), 80-150, Springer Zbl0405.55021
  2. A. Dold, D. Puppe, Homologie nicht-additiver Funktoren. Anwendungen., Annales de l'Institut Fourier (Grenoble) 11 (1961), 201-312 Zbl0098.36005MR150183
  3. S. Eilenberg, S. MacLane, Homology theory for multiplicative systems, Transactions of the AMS 71 (1951), 294-330 Zbl0043.25403MR43774
  4. S. Eilenberg, S. MacLane, On the groups H ( π , n ) , II, Annals of Mathematics 60 (1954), 49-139 Zbl0055.41704MR65162
  5. T. Goodwillie, Calculus. I: The first derivative of pseudoisotopy theory Zbl0741.57021MR1076523
  6. L. Illusie, Complexe cotangent et déformations II, 283 (1972), Springer Zbl0238.13017MR491681
  7. B. Johnson, R. McCarthy, Taylor towers for functors of additive categories, Journal of Pure and Applied Algebra 137 (1999), 253-284 Zbl0929.18007MR1685140
  8. B. Johnson, R. McCarthy, Deriving calculus with cotripels, (1999) Zbl1028.18004MR1685140
  9. M. Jibladze, T. Pirashvili, Cohomology of algebraic theories, Journal of Algebra 137 (1991), 253-296 Zbl0724.18005MR1094244
  10. W. Lück, Transformation groups and algebraic K-theory, 1408 (1989), Springer Zbl0679.57022MR1027600
  11. T. Pirashvili, Kan extension and stable homology of Eilenberg and Mac Lane spaces, Topology 35 (1996), 883-886 Zbl0858.55006MR1404915
  12. T. Pirashvili, Dold-Kan type theorem for Γ -groups, Mathematische Annalen 318 (2000), 277-298 Zbl0963.18006MR1795563
  13. T. Pirashvili, Hodge decomposition for higher order Hochschild homology, Annales Scientifiques de l'École Normale Supérieure 33 (2000), 151-179 Zbl0957.18004MR1755114
  14. B. Richter, Dissertation 332 (2000), Universität Bonn Zbl0967.55015
  15. O. Renaudin, Localisation homotopique et foncteurs entre espaces vectoriels, (janvier 2000) 
  16. P.G. Goerss, J.F. Jardine, Simplicial homotopy theory, (1999), Birhäuser Zbl0949.55001MR1711612
  17. T. Goodwillie, Calculus. II: Analytic functors Zbl0776.55008MR1162445
  18. T. Goodwillie, Calculus. III: The Taylor series of a homotopy functor Zbl1067.55006MR2026544

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