Rational nilpotent groups as subgroups of self-homotopy equivalences

Salvina Piccarreta

Cahiers de Topologie et Géométrie Différentielle Catégoriques (2001)

  • Volume: 42, Issue: 2, page 137-153
  • ISSN: 1245-530X

How to cite

top

Piccarreta, Salvina. "Rational nilpotent groups as subgroups of self-homotopy equivalences." Cahiers de Topologie et Géométrie Différentielle Catégoriques 42.2 (2001): 137-153. <http://eudml.org/doc/91643>.

@article{Piccarreta2001,
author = {Piccarreta, Salvina},
journal = {Cahiers de Topologie et Géométrie Différentielle Catégoriques},
keywords = {rational homotopy; realization problem},
language = {eng},
number = {2},
pages = {137-153},
publisher = {Dunod éditeur, publié avec le concours du CNRS},
title = {Rational nilpotent groups as subgroups of self-homotopy equivalences},
url = {http://eudml.org/doc/91643},
volume = {42},
year = {2001},
}

TY - JOUR
AU - Piccarreta, Salvina
TI - Rational nilpotent groups as subgroups of self-homotopy equivalences
JO - Cahiers de Topologie et Géométrie Différentielle Catégoriques
PY - 2001
PB - Dunod éditeur, publié avec le concours du CNRS
VL - 42
IS - 2
SP - 137
EP - 153
LA - eng
KW - rational homotopy; realization problem
UR - http://eudml.org/doc/91643
ER -

References

top
  1. [1] M. Arkowitz, The Group of Self-Homotopy Equivalences - a survey, in: Groups of Self-Equivalences and Related Topics, Lectures Notes in Mathematics, Vol. 1425 (Springer, Berlin, 1990), 170-203. Zbl0713.55004MR1070585
  2. [2] M. Arkowitz, C.R. Curjel, Groups of Homotopy classes, Lectures Notes in Mathematics (Springer, Berlin, 1967). Zbl0131.20502MR214061
  3. [3] M. Arkowitz, C.R. Curjel, The group of Homotopy Equivalences of a Space, Bull. Amer. Math. Soc., 70 (1964), 293-296. Zbl0129.15401MR163313
  4. [4] M. Arkowitz, G. Lupton, Equivalence Classes of Homotopy-Associative Comultiplications of Finite Complexes, Journal of Pure and Applied Alg.102 (1995), 109-136. Zbl0862.57026MR1354057
  5. [5] M. Arkowitz, G. Lupton, On Finiteness of Subgroups of Self-Homotopy Equivalences, Contemp. Math.181 (1995), 1-25. Zbl0830.55010MR1320984
  6. [6] M. Arkowitz, G. Lupton, On the Nilpotency of Subgroups of Self-Homotopy Equivalences, Prog. in Math.136 (1996), 1-22. Zbl0851.55017MR1397718
  7. [7] G. Baumslag, Lecture Notes on Nilpotent groups, Regional Conference Series in Mathematics (American Mathematical Society, Providence, 1971). Zbl0241.20001MR283082
  8. [8] P. Deligne, P. Griffiths, J. Morgan, D. Sullivan, RealHomotopy Theory of Kähler Manifolds, Invent. Math., 29 (1975), 245-274. Zbl0312.55011MR382702
  9. [9] E. Dror-Farjoun, A. Zabrodsky, Unipotency and Nilpotency in Homotopy Equivalences, Topology, 18 (1979), 187-197. Zbl0417.55008MR546789
  10. [10] W.H. Greub, S. Halperin, J.K. Vanstone, Connections, curvature and cohomology, vol. III (Academic Press, New York, 1975). Zbl0372.57001
  11. [11] P. Griffiths, J. Morgan, Rational Homotopy Theory and Differential Forms, Progress in Math. Vol. 15 (Birkhäuser, Boston, 1981). Zbl0474.55001MR641551
  12. [12] F. Grunewald, J. O'Halloran, Nilpotent Groups and Unipotent Algebraic Groups, J. of Pure and Applied Algebra37 (1985), 299-313. Zbl0576.20019MR797867
  13. [13] F. Grunewald, R. Scharlau, A Note on Finitely Generated Torsion-free Nilpotent Groups of Class 2, J. Algebra58 (1979), 162-175. Zbl0406.20031MR535851
  14. [14] F. Grunewald, D. Segal, L. Sterling, Nilpotent Groups of Hirsch Length Six, Math. Z.179 (1982), 219-235. Zbl0497.20026MR645498
  15. [15] P. Hall, The Edmonton Notes on Nilpotent Groups. Queen Mary College, Mathematics Notes (Mathematics Department Queen Mary College, London, 1969). Zbl0211.34201MR283083
  16. [16] S. Halperin, J. Stasheff, Obstructions to Homotopy Equivalences, Adv. in Math.32 (1979), 233-279. Zbl0408.55009MR539532
  17. [17] P.J. Hilton, On the Homotopy Groups of the Union of Spheres, J. London Math. Soc.30 (1955), 154-172. Zbl0064.17301MR68218
  18. [18] P.J. Hilton, G. Mislin, J. Roitberg, Localization of Nilpotent Groups and Spaces, Notas de Matematica, 15 (North Holland, Amsterdam, 1975). Zbl0323.55016
  19. [19] K.I. Maruyama, Localization of a Certain Subgroups of Self-Homotopy Equivalences, Pac. J. of Math136 (1989), 293-301. Zbl0673.55006MR978616
  20. [20] K.-I. Maruyama, Finiteness Properties of Self-Homotopy Equivalences Inducing the Identity on Homology, Math. Proc. Camb. Phil. Soc., 108 (1990), 291-297. Zbl0718.55006MR1074715
  21. [21] J. Neisendorfer, T.J. Miller, Formal and Coformal Spaces, Illinois J. Math22 (1978), 565-580. Zbl0396.55011MR500938
  22. [22] J.-P. Serre, Lie Algebras and LieGroups (Benjamin, New York, 1965). Zbl0132.27803MR218496
  23. [23] D. Tanré, Homotopie Rationelle: Modèles de Chen, Quillen, Sullivan, Lectures Notes in Mathematics, Vol. 1025 (Springer, Berlin, 1983). Zbl0539.55001MR764769

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.