K-theory of real Grassmann manifolds

2022/04/20 by Sudeep Podder, Podder, Sudeep, Parameswaran Sankaran +1
Mathematics · Physics and Astronomy · #20F65 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Analysis and Curvature Flows #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2204.09441

openalex publication_date 2022/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G_n,k denote the real Grassmann manifold of k-dimensional vector subspaces of \mathbb Rⁿ. Using the Hodgkin spectral sequence, we compute the complex K-ring of G_n,k, up to a small indeterminacy, for all values of n,k where 2≤ k≤ n-2. When n≡ 0 \mod 4, k≡ 1 \mod 2 our result is complete.

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