Geodesic
Determination of Grassmann Manifolds Which are Boundaries
Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 119-122

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

Let FGn,k denote the Grassmann manifold of all k-dimensional (left) F-vector subspace of Fn for F = R, the reals, C, the complex numbers, or H the quaternions. The problem of determining which of the Grassmannians bound was addressed by the author in [4]. Partial results were obtained in [4] for the case F = R, including a sufficient condition, due to A. Dold, on n and k for R Gn,k to bound. Here, we show that Dold's condition is also necessary, and obtain a new proof of sufficiency using the methods of this paper, which cover the complex and quaternionic cases as well.
DOI : 10.4153/CMB-1991-019-8
Mots-clés : 57R75. 
Sankaran, Parameswaran. Determination of Grassmann Manifolds Which are Boundaries. Canadian mathematical bulletin, Tome 34 (1991) no. 1, pp. 119-122. doi: 10.4153/CMB-1991-019-8
@article{10_4153_CMB_1991_019_8,
     author = {Sankaran, Parameswaran},
     title = {Determination of {Grassmann} {Manifolds} {Which} are {Boundaries}},
     journal = {Canadian mathematical bulletin},
     pages = {119--122},
     year = {1991},
     volume = {34},
     number = {1},
     doi = {10.4153/CMB-1991-019-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-019-8/}
}
TY  - JOUR
AU  - Sankaran, Parameswaran
TI  - Determination of Grassmann Manifolds Which are Boundaries
JO  - Canadian mathematical bulletin
PY  - 1991
SP  - 119
EP  - 122
VL  - 34
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-019-8/
DO  - 10.4153/CMB-1991-019-8
ID  - 10_4153_CMB_1991_019_8
ER  - 
%0 Journal Article
%A Sankaran, Parameswaran
%T Determination of Grassmann Manifolds Which are Boundaries
%J Canadian mathematical bulletin
%D 1991
%P 119-122
%V 34
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CMB-1991-019-8/
%R 10.4153/CMB-1991-019-8
%F 10_4153_CMB_1991_019_8

[1] 1. Conner, P. E., Differentiable periodic maps. 2nd ed., L.N.M. - 738, Springer-Verlag, 1979. Google Scholar

[2] 2. Lam, K. Y., A formula for the tangent bundle of flag manifolds and related manifolds, Trans. Amer. Math. Soc. 213 (1975), 305–314. Google Scholar

[3] 3. Milnor, J. W. and Stasheff, J. D., Characteristic classes, Ann. Math. Studies 76( 1974), Princeton Univ. Press, Princeton, N. J. Google Scholar

[4] 4. Sankaran, P., Which Grassmannians bound?, Arch. Math. 50 (1988), 474–476. Google Scholar

[5] 5 Sankaran, P., Cobordism of flag manifolds, submitted to Arch. Math. Google Scholar

[6] 6. Stong, R. E., Cup products in G rassmannians, Topology and App. 13 (1982), 103–113. Google Scholar

Cité par Sources :