Nilpotency of self homotopy equivalences with coefficients

Maxence Cuvilliez[1]; Aniceto Murillo[2]; Antonio Viruel[3]

  • [1] Universidad de Málaga Departamento de Álgebra, Geometría y Topología Ap. 59, 29080 Málaga (Spain)
  • [2] Universidad de Málaga Departamento de Álgebra, Geometría y Topología Ap. 59, 29080 Málaga, SPAIN
  • [3] Universidad de Málaga, Departamento de Álgebra, Geometría y Topología, Ap. 59, 29080 Málaga, SPAIN.

Annales de l’institut Fourier (2011)

  • Volume: 61, Issue: 1, page 351-364
  • ISSN: 0373-0956

Abstract

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In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.

How to cite

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Cuvilliez, Maxence, Murillo, Aniceto, and Viruel, Antonio. "Nilpotency of self homotopy equivalences with coefficients." Annales de l’institut Fourier 61.1 (2011): 351-364. <http://eudml.org/doc/219750>.

@article{Cuvilliez2011,
abstract = {In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.},
affiliation = {Universidad de Málaga Departamento de Álgebra, Geometría y Topología Ap. 59, 29080 Málaga (Spain); Universidad de Málaga Departamento de Álgebra, Geometría y Topología Ap. 59, 29080 Málaga, SPAIN; Universidad de Málaga, Departamento de Álgebra, Geometría y Topología, Ap. 59, 29080 Málaga, SPAIN.},
author = {Cuvilliez, Maxence, Murillo, Aniceto, Viruel, Antonio},
journal = {Annales de l’institut Fourier},
keywords = {Self homotopy equivalence; self-homotopy equivalence; nilpotency; space with local coefficients},
language = {eng},
number = {1},
pages = {351-364},
publisher = {Association des Annales de l’institut Fourier},
title = {Nilpotency of self homotopy equivalences with coefficients},
url = {http://eudml.org/doc/219750},
volume = {61},
year = {2011},
}

TY - JOUR
AU - Cuvilliez, Maxence
AU - Murillo, Aniceto
AU - Viruel, Antonio
TI - Nilpotency of self homotopy equivalences with coefficients
JO - Annales de l’institut Fourier
PY - 2011
PB - Association des Annales de l’institut Fourier
VL - 61
IS - 1
SP - 351
EP - 364
AB - In this paper we study the nilpotency of certain groups of self homotopy equivalences. Our main goal is to extend, to localized homotopy groups and/or homotopy groups with coefficients, the general principle of Dror and Zabrodsky by which a group of self homotopy equivalences of a finite complex which acts nilpotently on the homotopy groups is itself nilpotent.
LA - eng
KW - Self homotopy equivalence; self-homotopy equivalence; nilpotency; space with local coefficients
UR - http://eudml.org/doc/219750
ER -

References

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  14. J. Møller, Self-homotopy equivalences of H * ( - ; ℤ / p ) -local spaces, Koday Math. Jour. 12 (1989), 270-281 Zbl0685.55005MR1002667
  15. J. Rutter, Homotopy self–equivalences 1988–1999, Contemporary Math. 274 (2001), 1-12 Zbl0973.55001MR1816998
  16. H. Scheerer, D. Tanré, Variation zum Konzept der Lusternik-Schnirelmann Kategorie, Math. Nachr. 207 (1999), 183-194 Zbl0933.55003MR1724294
  17. J. Siegel, k -invariants in local coefficients theory, Proc. Amer. Math. Soc. 29 (1971), 169-174 Zbl0214.49903MR307224
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