Orbit spaces for torus actions on Hessenberg varieties

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 $S^{n+1} \setminus (U_1 \sqcup \dots \sqcup U_l)$, 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.