ON THE MORAVA -THEORY OF THE REAL GRASSMANNIAN
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Abstract
The main purpose of this paper is to determine an explicit -basis for the th Morava -theory of the real Grassmannian for integers and . Using Lenart’s combinatorial formula, we compute the action of the primitive Milnor operation on Schur functions to determine the -homology of the mod cohomology of , thereby determining the -term of the Atiyah-Hirzebruch spectral sequence. We show that the size of the -term equals the lower bound for the size of defined by Kuhn and Lloyd (2024); therefore, the spectral sequence collapses at the -term. This result provides foundational data for further investigations of Morava -theory of real Grassmannians.
Keywords
Atiyah-Hirzebruch spectral sequence, Morava K-theory, Real Grassmannian
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References
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