On the Morava K-theory of the real Grassmannian Gr_2(R^m)
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Abstract
The main purpose of the paper is to determine an explicit K(n)-basis of the nth Morava K-theory of the real Grassmannian Gr_2(R^m) for integer numbers n>0 and m>=0.
Keywords
Real Grassmannian, Morava K-theory, Atiyah-Hirzebruch spectral sequence.
Article Details
References
[1] P. H. Chơn and N. Đ. H. Hai, On the Morava K-thoery of the real Grassmannian Gr_3(R^m), preprint (2025).
[2] H. Hiller, Geometry of Coxeter groups, Research Notes in Mathematics, vol. 54, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982.
[3] N. J. Kuhn and C. J. R. Lloyd, Computing the Morava K-theory of real Grassmannians using chromatic fixed point theory, Algebr. Geom. Topol. 24 (2024), no. 2, 919--950.
[4] C. Lenart, The combinatorics of Steenrod operations on the cohomology of Grassmannians, Adv. Math. 136 (1998), no. 2, 251-283.
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[7] N. Yagita, On the Steenrod algebra of Morava K-theory, J. London Math. Soc. (2) 22 (1980), no. 3, 423-438.
[2] H. Hiller, Geometry of Coxeter groups, Research Notes in Mathematics, vol. 54, Pitman (Advanced Publishing Program), Boston, Mass.-London, 1982.
[3] N. J. Kuhn and C. J. R. Lloyd, Computing the Morava K-theory of real Grassmannians using chromatic fixed point theory, Algebr. Geom. Topol. 24 (2024), no. 2, 919--950.
[4] C. Lenart, The combinatorics of Steenrod operations on the cohomology of Grassmannians, Adv. Math. 136 (1998), no. 2, 251-283.
[5] I. G. Macdonald, Symmetric functions and Hall polynomials, second ed., Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1995, With contributions by A. Zelevinsky, Oxford Science Publications.
[6] J. W. Milnor and J. D. Stasheff, Characteristic classes, Princeton University Press, Princeton, N. J.; University of Tokyo Press, Tokyo, 1974, Annals of Mathematics Studies, No. 76.
[7] N. Yagita, On the Steenrod algebra of Morava K-theory, J. London Math. Soc. (2) 22 (1980), no. 3, 423-438.