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Symplectomorphism group of $T^\ast (G_{\mathbb{C}} / B)$ and the braid group I: a homotopy equivalence for $G_{\mathbb{C}} = SL_3 (\mathbb{C})$
2019
The Journal of Symplectic Geometry
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For a semisimple Lie group G C over 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 C = SL 3 (C), under the SU (3)-equivariance condition on symplectomorphisms. 1 Introduction 337 2 Preliminaries and Set-ups 343 3 Construction of the surjective homomorphism β G : Sympl G Z (T * B) → B W , G = SU (n) 348 4 β G is a homotopy equivalence for G = SU (3) 359 References 379
doi:10.4310/jsg.2019.v17.n2.a2
fatcat:6cd72zagvfeqvfbejoxvs7ehcq