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arXiv · 1412.0511

Symplectomorphism group of $T^*(G_\mathbb{C}/B)$ and the braid group I: a homotopy equivalence for $G_\mathbb{C}=SL_3(\mathbb{C})$

Xin Jin
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Abstract

For a semisimple Lie group $G_\mathbb{C}$ over $\mathbb{C}$, we study the homotopy type of the symplectomorphism group of the cotangent bundle of the flag variety and its relation to the braid group. We prove a homotopy equivalence between the two groups in the case of $G_\mathbb{C}=SL_3(\mathbb{C})$, under the $SU(3)$-equivariancy condition on symplectomorphisms.

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Xin Jin. 2014-12-01. Symplectomorphism group of $T^*(G_\mathbb{C}/B)$ and the braid group I: a homotopy equivalence for $G_\mathbb{C}=SL_3(\mathbb{C})$. https://doi.org/10.4310/jsg.2019.v17.n2.a2

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