Geodesic
Rational Classification of Simple Function Space Components for Flag Manifolds
Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 855-864

Voir la notice de l'article provenant de la source Cambridge University Press

LetM(X, Y) denote the space of all continuous functions between X and Y and Mƒ(X, Y) the path component corresponding to a given map ƒ : X → Y. When X and Y are classical flag manifolds, we prove the components of M(X, Y) corresponding to “simple” maps ƒ are classified up to rational homotopy type by the dimension of the kernel of ƒ in degree two cohomology. In fact, these components are themselves all products of flag manifolds and odd spheres.
DOI : 10.4153/CJM-1997-044-1
Mots-clés : 55P62, 55P15, 58D99, Rational homotopy theory, Sullivan-Haefliger model 
Smith, Samuel Bruce. Rational Classification of Simple Function Space Components for Flag Manifolds. Canadian journal of mathematics, Tome 49 (1997) no. 4, pp. 855-864. doi: 10.4153/CJM-1997-044-1
@article{10_4153_CJM_1997_044_1,
     author = {Smith, Samuel Bruce},
     title = {Rational {Classification} of {Simple} {Function} {Space} {Components} for {Flag} {Manifolds}},
     journal = {Canadian journal of mathematics},
     pages = {855--864},
     year = {1997},
     volume = {49},
     number = {4},
     doi = {10.4153/CJM-1997-044-1},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-044-1/}
}
TY  - JOUR
AU  - Smith, Samuel Bruce
TI  - Rational Classification of Simple Function Space Components for Flag Manifolds
JO  - Canadian journal of mathematics
PY  - 1997
SP  - 855
EP  - 864
VL  - 49
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-044-1/
DO  - 10.4153/CJM-1997-044-1
ID  - 10_4153_CJM_1997_044_1
ER  - 
%0 Journal Article
%A Smith, Samuel Bruce
%T Rational Classification of Simple Function Space Components for Flag Manifolds
%J Canadian journal of mathematics
%D 1997
%P 855-864
%V 49
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1997-044-1/
%R 10.4153/CJM-1997-044-1
%F 10_4153_CJM_1997_044_1

[1] 1. Arkowitz, M. and Lupton, G., On finiteness of subgroups of self-homotopy equivalences. Contemp. Math. 181(1995), 1–25. Google Scholar

[2] 2. Borel, A., Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts. Ann. of Math. 57(1953), 115–207. Google Scholar

[3] 3. Deligne, P., Griffiths, P., Morgan, J., Sullivan, D., Real homotopy theory of Kähler manifolds. Invent. Math. (3) 29(1975), 245–275. Google Scholar

[4] 4. Glover, H. and Homer, W., Self-maps of flag manifolds. Trans. Amer.Math. Soc., 267(1981), 423–434. Google Scholar

[5] 5. Haefliger, A., Rational homotopy of the space of sections of a nilpotent bundle. Trans. Amer. Math. Soc. 273(1982), 609–620. Google Scholar

[6] 6. Halperin, S., Finiteness in the minimal models of Sullivan. Trans. Amer.Math. Soc. 230(1977), 173–199. Google Scholar

[7] 7. Hilton, P., Mislin, G., Roitberg, J., Steiner, R., On free maps and free homotopies into nilpotent spaces. Lecture Notes in Math., 673(1978), 202–218. Springer-Verlag, New York. Google Scholar

[8] 8. Humphreys, J., Reflection groups and Coxeter groups. Cambridge Studies in Advanced Math. vol. 29, Cambridge Univ. Press, New York, 1990. Google Scholar

[9] 9. Liulevicius, A., Flag manifolds and homotopy rigidity of linear actions. Lecture Notes inMath., 673(1978), 254–261. Springer-Verlag, New York. Google Scholar

[10] 10. Meier, W., Rational universal fibrations and flag manifolds. Math. Ann. 258(1982), 329–340. Google Scholar

[11] 11. Møller, J.M. and Raussen, M., Rational homotopy of spaces of maps into spheres and complex projective spaces. Trans. Amer. Math. Soc. (2) 292(1985), 721–732. Google Scholar

[12] 12. Shiga, H. and Tezuka, M., Rational fibrations, homogeneous spaces with positive Euler characteristic and Jacobians. Ann. Inst. Fourier Grenoble 37(1987), 81–106. Google Scholar

[13] 13. Smith, S., Rational homotopy of the space of self-maps of complexes with finitely many homotopy groups. Trans. Amer. Math. Soc. 342(1994), 895–91. Google Scholar

[14] 14. Smith, S., L.S. Rational category of function space components for F0-spaces. In preparation. Google Scholar

[15] 15. Thom, R., L’homologie des espaces fonctionelles. Colloque de Topologie Algébrique, Louvain, 1956. 29–39. Google Scholar

Cité par Sources :