The complex K ring of the flip Stiefel manifolds

2024/04/24 by Samik Basu, Basu, Samik, Shilpa Gondhali +3
Mathematics · Computer Science · #Commutative Algebra and Its Applications #Topological and Geometric Data Analysis #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.2404.15803

Abstract

The flip Stiefel manifolds (FV_m,2s) are defined as the quotient of the real Stiefel manifolds (V_m,2s) induced by the simultaneous pairwise flipping of the co-ordinates by the cyclic group of order 2. We calculate the complex (K)-ring of the flip Stiefel manifolds, K^∗(FV_m,2s), for s even. Standard techniques involve the representation theory of Spin(m), and the Hodgkin spectral sequence. However, the non-trivial element inducing the action doesn't readily yield the desired homomorphisms. Hence, by performing additional analysis, we settle the question for the case of (s ≡ 0 \pmod 2.)

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