$K$-theory of oriented Grassmann manifolds
Mathematica slovaca, Tome 47 (1997) no. 3, pp. 319-338
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Classification : 19L64, 53C15, 55N15, 57R25
@article{MASLO_1997_47_3_a9,
     author = {Sankaran, Parameswaran and Zvengrowski, Peter},
     title = {$K$-theory of oriented {Grassmann} manifolds},
     journal = {Mathematica slovaca},
     pages = {319--338},
     year = {1997},
     volume = {47},
     number = {3},
     mrnumber = {1796336},
     zbl = {1022.55004},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MASLO_1997_47_3_a9/}
}
TY  - JOUR
AU  - Sankaran, Parameswaran
AU  - Zvengrowski, Peter
TI  - $K$-theory of oriented Grassmann manifolds
JO  - Mathematica slovaca
PY  - 1997
SP  - 319
EP  - 338
VL  - 47
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/MASLO_1997_47_3_a9/
LA  - en
ID  - MASLO_1997_47_3_a9
ER  - 
%0 Journal Article
%A Sankaran, Parameswaran
%A Zvengrowski, Peter
%T $K$-theory of oriented Grassmann manifolds
%J Mathematica slovaca
%D 1997
%P 319-338
%V 47
%N 3
%U http://geodesic.mathdoc.fr/item/MASLO_1997_47_3_a9/
%G en
%F MASLO_1997_47_3_a9
Sankaran, Parameswaran; Zvengrowski, Peter. $K$-theory of oriented Grassmann manifolds. Mathematica slovaca, Tome 47 (1997) no. 3, pp. 319-338. http://geodesic.mathdoc.fr/item/MASLO_1997_47_3_a9/

[1] ANTONIANO E.-GITLER S.-UCCI J.-ZVENGROWSKI P.: On the K-theory and parallelizability of projective Stiefel manifolds. Bol. Soc. Mat. Mexicana (2) 31 (1986), 29-46. | MR | Zbl

[2] ATIYAH M. F.- HIRZEBRUCH F.: Vector bundles and homogeneous. In: Proc. Symp. Pure Math. 3, 1961, pp. 7-38.

[3] ATIYAH M. F.-MacDONALD I. G.: Introduction to Commutative Algebra. Addison-Wesley, Reading, 1969. | MR | Zbl

[4] BOREL A.-SERRE J.-P.: Groupes de Lie et puissances reduites de Steenrod. Amer. J. Math. 75 (1953), 409-448. | MR

[5] BOREL A.-HIRZEBRUCH F.: Characteristic classes and homogeneous spaces I. Amer. J. Math. 80 (1958), 458-538. | MR

[6] BRÖCKER T.-TOM DIECK T.: Representations of Compact Lie Groups. Grad. Texts in Math. 98, Springer-Verlag, New York, 1985. | MR

[7] CARTAN H.-EILENBERG S.: Homological Algebra. Princeton University Pгess, Princeton, 1956. | MR | Zbl

[8] HODGKIN L.: The equivariant Künneth theorem in K-theory. Lecture Notes in Math. 496, Springer-Verlag, New York, 1975. | MR | Zbl

[9] HOGGAR S. G.: On KO theory of Grassmannians. Quart. J. Math. Oxford Ser. (2) 20 (1969), 447-463. | MR | Zbl

[10] HUSEMOLLER D.: Fibre Bundles. Grad. Texts in Math. 20, Springer-Verlag, New York, 1975. | MR | Zbl

[11] KORBAS J.-ZVENGROWSKI P.: The vector field problem: a survey with emphasis on specific manifolds. Exposition. Math. 12 (1994), 3-30. | MR | Zbl

[12] KULTZE R.: An elementary proof for the non-parallelizabiltiy of oriented Grassmannians. Note Mat. 10, Suppl. 2 (1990), 363-367. | MR

[13] LAM K. Y.: A formula for the tangent bundle of flag manifolds and related manifolds. Trans. Amer. Math. Soc. 213 (1975), 305-314. | MR | Zbl

[14] MacLANE S.: Homology. Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 114, Springer Verlag, Berlin, 1967. | MR

[15] MIATELLO I. D.-MIATELLO R. J.: On stable parallelizability of Gkn and related manifolds. Math. Ann. 259 (1982), 343-350. | MR

[16] PITTIE H.: Homogeneous vector bundles on homogeneous spaces. Topology II (1972), 199-203. | MR | Zbl

[17] ROUX A.: Application de la suite spectrale d'Hodgkin au calcul de la K-theorie des varietes de Stiefel. Bull. Soc. Math. France 99 (1971), 345-368. | MR | Zbl

[18] SANKARAN P.: Nonexistence of almost complex structures on Grassmann manifolds. Proc. Amer. Math. Soc. 113 (1991), 297-302. | MR | Zbl

[19] SANKARAN P.-ZVENGROWSKI P.: Stable parallelizability of partially oriented flag manifolds. Pacific J. Math. 128 (1987), 349-359. | MR | Zbl

[20] SPANIER E. H.: Algebraic Topology. McGraw-Hill Book Company, New York-San Francisco-St. Louis-Toronto-London-Sydney, 1966. | MR | Zbl

[21] STEENROD N.: Topology of Fibre Bundles. Princeton Univ. Press, Princeton, 1951. | MR | Zbl

[22] TANG, ZI-ZHOU: Non-existence of weak almost complex structures on Grassmannians. Max Planck Inst. Preprint 92-87.