Email this article Orbit spaces for torus actions on Hessenberg varieties
- Authors: Cherepanov V.V.1
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Affiliations:
- Faculty of Computer Science, National Research University "Higher School of Economics"
- Issue: Vol 212, No 12 (2021)
- Pages: 115-136
- Section: Articles
- URL: https://ogarev-online.ru/0368-8666/article/view/133420
- DOI: https://doi.org/10.4213/sm9278
- ID: 133420
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Abstract
In this paper we study effective actions of the compact torus $T^{n-1}$ on smooth compact manifolds $M^{2n}$ of even dimension with isolated fixed points. It is proved that under certain conditions on the weight vectors of the tangent representation, the orbit space of such an action is a manifold with corners. In the case of Hamiltonian actions, the orbit space is homotopy equivalent to $S^{n+1} \setminus (U_1 \sqcup …\sqcup U_l)$, the complement to the union of disjoint open subsets of the $(n + 1)$-sphere. The results obtained are applied to regular Hessenberg varieties and isospectral manifolds of Hermitian matrices of step type. Bibliography: 23 titles.
About the authors
Vladislav Vladimirovich Cherepanov
Faculty of Computer Science, National Research University "Higher School of Economics"without scientific degree, Scientific Employee
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