Basic constructions in rational homotopy theory of function spaces

Urtzi Buijs[1]; Aniceto Murillo[2]

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

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 3, page 815-838
  • ISSN: 0373-0956

Abstract

top
Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.

How to cite

top

Buijs, Urtzi, and Murillo, Aniceto. "Basic constructions in rational homotopy theory of function spaces." Annales de l’institut Fourier 56.3 (2006): 815-838. <http://eudml.org/doc/10165>.

@article{Buijs2006,
abstract = {Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.},
affiliation = {Universidad de Málaga Departamento de Algebra Geometría y Topología Ap. 59, 29080 Málaga (Spain); Departamento de Algebra, Geometría y Topología, Universidad de Málaga, Ap. 59, 29080 Málaga, Spain},
author = {Buijs, Urtzi, Murillo, Aniceto},
journal = {Annales de l’institut Fourier},
keywords = {Function space; mapping space; Sullivan model; rational homotopy theory; function space},
language = {eng},
number = {3},
pages = {815-838},
publisher = {Association des Annales de l’institut Fourier},
title = {Basic constructions in rational homotopy theory of function spaces},
url = {http://eudml.org/doc/10165},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Buijs, Urtzi
AU - Murillo, Aniceto
TI - Basic constructions in rational homotopy theory of function spaces
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 3
SP - 815
EP - 838
AB - Via the Bousfield-Gugenheim realization functor, and starting from the Brown-Szczarba model of a function space, we give a functorial framework to describe basic objects and maps concerning the rational homotopy type of function spaces and its path components.
LA - eng
KW - Function space; mapping space; Sullivan model; rational homotopy theory; function space
UR - http://eudml.org/doc/10165
ER -

References

top
  1. A. K. Bousfield, V. K. A. M. Gugenheim, On PL De Rham theory and rational homotopy type, 179 (8) (1976), Memoirs of the Amer. Math. Soc. Zbl0338.55008MR425956
  2. E. H. Brown, R. H. Szczarba, Continuous cohomology and real homotopy type, Trans. Amer. Math. Soc. 31 (1989), 57-106 Zbl0671.55006MR929667
  3. E. H. Brown, R. H. Szczarba, On the rational homotopy type of function spaces, Trans. Amer. Math. Soc. 349 (1997), 4931-4951 Zbl0927.55012MR1407482
  4. Y. Félix, Rational category of the space of sections of a nilpotent bundle, Comment. Math. Helvetici 65 (1990), 615-622 Zbl0715.55009MR1078101
  5. Y. Félix, S. Halperin, J.C. Thomas, Rational Homotopy Theory, G.T.M. 205 (2000), Springer Zbl0961.55002MR1802847
  6. P. G. Goerss, J. F. Jardine, Simplicial Homotopy Theory, Progress in Mathematics 174 (1999), Birkhäuser, Basel-Boston-Berlin Zbl0949.55001MR1711612
  7. A. Haefliger, Rational homotopy of the space of sections of a nilpotent bundle, Trans. Amer. Math. Soc. 273 (1982), 609-620 Zbl0508.55019MR667163
  8. S. Halperin, Lecture on Minimal Models, 230 (1983), Mémoires de la Société Mathématique de France Zbl0536.55003
  9. P. Hilton, G. Mislin, J. Roitberg, Localization of nilpotent groups and spaces, 15 (1975), North Holland Mathematical Studies Zbl0323.55016MR478146
  10. K. Kuribayashi, A rational model for the evaluation map, (2005) Zbl1097.18004
  11. J. P. May, Simplicial Objects in Algebraic Topology, (1992), Chicago Lectures in Mathematics Zbl0769.55001MR1206474
  12. J. Milnor, On spaces having the homotopy type of a CW-complex, Trans. Amer. Math. Soc. 342 (1994), 895-915 
  13. S. Smith, Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups, Trans. Amer. Math. Soc. 90 (1994), 272-280 Zbl0802.55009
  14. S. Smith, Rational evaluation subgroups, Math. Zeit. 221 (1996), 387-400 Zbl0855.55009MR1381587
  15. D. Sullivan, Infinitesimal computations in Topology, Publ. Math. de l’I.H.E.S. 47 (1978), 269-331 Zbl0374.57002MR646078
  16. R. Thom, L’homologie des espaces fonctionnels, Colloque de topologie algébrique (1957), 29-39 Zbl0077.36301MR89408
  17. M. Vigué-Poirrier, Sur l’homotopie rationnelle des espaces fonctionnels, Manuscripta Math. 56 (1986), 177-191 Zbl0597.55008MR850369

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.