Cohomology of the universal centralizers I: the adjoint group case

Xin Jin

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arXiv · 2411.09041

Cohomology of the universal centralizers I: the adjoint group case

Xin Jin

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Abstract

We compute the rational cohomology of the universal centralizer $J_G$ (also known as the Toda system or BFM space) for a complex (connected) semisimple group $G$ of adjoint form. While $J_G$ exhibits interesting and increasingly complex topology as the rank of $G$ rises, its rational cohomology is surprisingly simple--it coincides with that of a point. In a subsequent work [Jin2], we will extend this analysis to the case of $J_G$ for general semisimple $G$. In particular, we will show that its rational cohomology has pure Hodge structure.

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Xin Jin. 2024-11-13. Cohomology of the universal centralizers I: the adjoint group case. https://arxiv.org/abs/2411.09041

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