K -theory of oriented Grassmann manifolds

Parameswaran Sankaran; Peter D. Zvengrowski

Mathematica Slovaca (1997)

  • Volume: 47, Issue: 3, page 319-338
  • ISSN: 0139-9918

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Sankaran, Parameswaran, and Zvengrowski, Peter D.. "$K$-theory of oriented Grassmann manifolds." Mathematica Slovaca 47.3 (1997): 319-338. <http://eudml.org/doc/31906>.

@article{Sankaran1997,
author = {Sankaran, Parameswaran, Zvengrowski, Peter D.},
journal = {Mathematica Slovaca},
keywords = {Grassmann manifold; K-theory; parallelizability; almost complex structure; flag manifold; Pontrjagin class; spinor representation; Hodgkin spectral sequence},
language = {eng},
number = {3},
pages = {319-338},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {$K$-theory of oriented Grassmann manifolds},
url = {http://eudml.org/doc/31906},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Sankaran, Parameswaran
AU - Zvengrowski, Peter D.
TI - $K$-theory of oriented Grassmann manifolds
JO - Mathematica Slovaca
PY - 1997
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 47
IS - 3
SP - 319
EP - 338
LA - eng
KW - Grassmann manifold; K-theory; parallelizability; almost complex structure; flag manifold; Pontrjagin class; spinor representation; Hodgkin spectral sequence
UR - http://eudml.org/doc/31906
ER -

References

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  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. (1986) Zbl0665.57017MR0946976
  2. ATIYAH M. F.- HIRZEBRUCH F., Vector bundles and homogeneous, In: Proc. Symp. Pure Math. 3, 1961, pp. 7-38. (1961) 
  3. ATIYAH M. F.-MacDONALD I. G., Introduction to Commutative Algebra, Addison-Wesley, Reading, 1969. (1969) Zbl0175.03601MR0242802
  4. BOREL A.-SERRE J.-P., Groupes de Lie et puissances reduites de Steenrod, Amer. J. Math. 75 (1953), 409-448. (1953) MR0058213
  5. BOREL A.-HIRZEBRUCH F., Characteristic classes and homogeneous spaces I, Amer. J. Math. 80 (1958), 458-538. (1958) MR0102800
  6. BRÖCKER T.-TOM DIECK T., Representations of Compact Lie Groups, Grad. Texts in Math. 98, Springer-Verlag, New York, 1985. (1985) MR0781344
  7. CARTAN H.-EILENBERG S., Homological Algebra, Princeton University Pгess, Princeton, 1956. (1956) Zbl0075.24305MR0077480
  8. HODGKIN L., The equivariant Künneth theorem in K-theory, Lecture Notes in Math. 496, Springer-Verlag, New York, 1975. (1975) Zbl0323.55009MR0478156
  9. HOGGAR S. G., On KO theory of Grassmannians, Quart. J. Math. Oxford Ser. (2) 20 (1969), 447-463. (1969) Zbl0184.48402MR0254841
  10. HUSEMOLLER D., Fibre Bundles, Grad. Texts in Math. 20, Springer-Verlag, New York, 1975. (1975) Zbl0307.55015MR0370578
  11. KORBAS J.-ZVENGROWSKI P., The vector field problem: a survey with emphasis on specific manifolds, Exposition. Math. 12 (1994), 3-30. (1994) Zbl0823.57001MR1267626
  12. KULTZE R., An elementary proof for the non-parallelizabiltiy of oriented Grassmannians, Note Mat. 10, Suppl. 2 (1990), 363-367. (1990) MR1221951
  13. LAM K. Y., A formula for the tangent bundle of flag manifolds and related manifolds, Trans. Amer. Math. Soc. 213 (1975), 305-314. (1975) Zbl0312.55020MR0431194
  14. MacLANE S., Homology, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 114, Springer Verlag, Berlin, 1967. (1967) MR0349792
  15. MIATELLO I. D.-MIATELLO R. J., On stable parallelizability of Gkn and related manifolds, Math. Ann. 259 (1982), 343-350. (1982) MR0661202
  16. PITTIE H., Homogeneous vector bundles on homogeneous spaces, Topology II (1972), 199-203. (1972) Zbl0229.57017MR0290402
  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. (1971) Zbl0228.55006MR0312500
  18. SANKARAN P., Nonexistence of almost complex structures on Grassmann manifolds, Proc. Amer. Math. Soc. 113 (1991), 297-302. (1991) Zbl0725.57011MR1043420
  19. SANKARAN P.-ZVENGROWSKI P., Stable parallelizability of partially oriented flag manifolds, Pacific J. Math. 128 (1987), 349-359. (1987) Zbl0592.57018MR0888523
  20. SPANIER E. H., Algebraic Topology, McGraw-Hill Book Company, New York-San Francisco-St. Louis-Toronto-London-Sydney, 1966. (1966) Zbl0145.43303MR0210112
  21. STEENROD N., Topology of Fibre Bundles, Princeton Univ. Press, Princeton, 1951. (1951) Zbl0054.07103MR0039258
  22. TANG, ZI-ZHOU, Non-existence of weak almost complex structures on Grassmannians, Max Planck Inst. Preprint 92-87. 

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