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arXiv · 1811.08288

The Gamma filtrations for the Spin groups

Nobuaki Yagita
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Abstract

Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we try to compute $gr_{\gamma}^*(G/T)$ the graded ring associated with the gamma filtration of the complex $K$-theory $K^0(G/T)$ for $G=Spin(n)$. In particular, we give a counterexample for a conjecture by Karpenko when $G=Spin(17)$. The arguments for $E_7$ in $\S 11$ of the old version were not correct, and they are deleted in this version.

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Nobuaki Yagita. 2018-11-17. The Gamma filtrations for the Spin groups. https://arxiv.org/abs/1811.08288

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