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arXiv · 2404.15803

The complex K ring of the flip Stiefel manifolds

Samik Basu·Shilpa Gondhali·Fathima Safikaa
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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, $K^\ast(FV_{m,2s})$, 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 \equiv 0 \pmod 2.)

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Samik Basu, Shilpa Gondhali, Fathima Safikaa. 2024-04-24. The complex K ring of the flip Stiefel manifolds. https://arxiv.org/abs/2404.15803

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